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148-1192: Artificial intelligence ( AI ), in its broadest sense, is intelligence exhibited by machines , particularly computer systems . It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. Such machines may be called AIs. Some high-profile applications of AI include advanced web search engines (e.g., Google Search ); recommendation systems (used by YouTube , Amazon , and Netflix ); interacting via human speech (e.g., Google Assistant , Siri , and Alexa ); autonomous vehicles (e.g., Waymo ); generative and creative tools (e.g., ChatGPT , and AI art ); and superhuman play and analysis in strategy games (e.g., chess and Go ). However, many AI applications are not perceived as AI: "A lot of cutting edge AI has filtered into general applications, often without being called AI because once something becomes useful enough and common enough it's not labeled AI anymore ." The various subfields of AI research are centered around particular goals and

296-415: A conditional statement ( P → Q {\displaystyle P\rightarrow Q} ) and as second premise the antecedent ( P {\displaystyle P} ) of the conditional statement. It obtains the consequent ( Q {\displaystyle Q} ) of the conditional statement as its conclusion. The argument form is listed below: In this form of deductive reasoning,

444-578: A loss function . Variants of gradient descent are commonly used to train neural networks. Another type of local search is evolutionary computation , which aims to iteratively improve a set of candidate solutions by "mutating" and "recombining" them, selecting only the fittest to survive each generation. Distributed search processes can coordinate via swarm intelligence algorithms. Two popular swarm algorithms used in search are particle swarm optimization (inspired by bird flocking ) and ant colony optimization (inspired by ant trails ). Formal logic

592-410: A speaker-determined definition of deduction since it depends also on the speaker whether the argument in question is deductive or not. For speakerless definitions, on the other hand, only the argument itself matters independent of the speaker. One advantage of this type of formulation is that it makes it possible to distinguish between good or valid and bad or invalid deductive arguments: the argument

740-402: A " hypersurface in a multidimensional space" to compare systems that are good at different intellectual tasks. Some skeptics believe that there is no meaningful way to define intelligence, aside from "just pointing to ourselves". Deductive reasoning Deductive logic studies under what conditions an argument is valid. According to the semantic approach, an argument is valid if there

888-473: A "degree of truth" between 0 and 1. It can therefore handle propositions that are vague and partially true. Non-monotonic logics , including logic programming with negation as failure , are designed to handle default reasoning . Other specialized versions of logic have been developed to describe many complex domains. Many problems in AI (including in reasoning, planning, learning, perception, and robotics) require

1036-402: A bachelor; therefore, Othello is not male". This is similar to the valid rule of inference called modus tollens , the difference being that the second premise and the conclusion are switched around. Other formal fallacies include affirming a disjunct , denying a conjunct , and the fallacy of the undistributed middle . All of them have in common that the truth of their premises does not ensure

1184-419: A certain pattern. These observations are then used to form a conclusion either about a yet unobserved entity or about a general law. For abductive inferences, the premises support the conclusion because the conclusion is the best explanation of why the premises are true. The support ampliative arguments provide for their conclusion comes in degrees: some ampliative arguments are stronger than others. This

1332-400: A conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises. If the reasoning was done correctly, it results in a valid deduction: the truth of the premises ensures the truth of the conclusion. For example, in the syllogistic argument "all frogs are amphibians; no cats are amphibians; therefore, no cats are frogs"

1480-412: A conditional statement (formula) and the negation of the consequent ( ¬ Q {\displaystyle \lnot Q} ) and as conclusion the negation of the antecedent ( ¬ P {\displaystyle \lnot P} ). In contrast to modus ponens , reasoning with modus tollens goes in the opposite direction to that of the conditional. The general expression for modus tollens

1628-458: A contradiction from premises that include the negation of the problem to be solved. Inference in both Horn clause logic and first-order logic is undecidable , and therefore intractable . However, backward reasoning with Horn clauses, which underpins computation in the logic programming language Prolog , is Turing complete . Moreover, its efficiency is competitive with computation in other symbolic programming languages. Fuzzy logic assigns

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1776-449: A different account of which inferences are valid. For example, the rule of inference known as double negation elimination , i.e. that if a proposition is not not true then it is also true , is accepted in classical logic but rejected in intuitionistic logic . Modus ponens (also known as "affirming the antecedent" or "the law of detachment") is the primary deductive rule of inference . It applies to arguments that have as first premise

1924-452: A fairly high degree of intellect that varies according to each species. The same is true with arthropods . Evidence of a general factor of intelligence has been observed in non-human animals. First described in humans , the g factor has since been identified in a number of non-human species. Cognitive ability and intelligence cannot be measured using the same, largely verbally dependent, scales developed for humans. Instead, intelligence

2072-533: A function and once the weight crosses its specified threshold, the data is transmitted to the next layer. A network is typically called a deep neural network if it has at least 2 hidden layers. Learning algorithms for neural networks use local search to choose the weights that will get the right output for each input during training. The most common training technique is the backpropagation algorithm. Neural networks learn to model complex relationships between inputs and outputs and find patterns in data. In theory,

2220-434: A fundamental quality possessed by every person is the theory of General Intelligence, or g factor . The g factor is a construct that summarizes the correlations observed between an individual's scores on a range of cognitive tests. Today, most psychologists agree that IQ measures at least some aspects of human intelligence, particularly the ability to thrive in an academic context. However, many psychologists question

2368-638: A given person's intellectual performance will vary on different occasions, in different domains, as judged by different criteria. Concepts of "intelligence" are attempts to clarify and organize this complex set of phenomena. Although considerable clarity has been achieved in some areas, no such conceptualization has yet answered all the important questions, and none commands universal assent. Indeed, when two dozen prominent theorists were recently asked to define intelligence, they gave two dozen, somewhat different, definitions. Psychologists and learning researchers also have suggested definitions of intelligence such as

2516-509: A logical constant may be introduced into a new sentence of the proof . For example, the introduction rule for the logical constant " ∧ {\displaystyle \land } " (and) is " A , B ( A ∧ B ) {\displaystyle {\frac {A,B}{(A\land B)}}} " . It expresses that, given the premises " A {\displaystyle A} " and " B {\displaystyle B} " individually, one may draw

2664-516: A neural network can learn any function. Intelligence Intelligence has been defined in many ways: the capacity for abstraction , logic , understanding , self-awareness , learning , emotional knowledge , reasoning , planning , creativity , critical thinking , and problem-solving . It can be described as the ability to perceive or infer information ; and to retain it as knowledge to be applied to adaptive behaviors within an environment or context. The term rose to prominence during

2812-425: A path to a target goal, a process called means-ends analysis . Simple exhaustive searches are rarely sufficient for most real-world problems: the search space (the number of places to search) quickly grows to astronomical numbers . The result is a search that is too slow or never completes. " Heuristics " or "rules of thumb" can help prioritize choices that are more likely to reach a goal. Adversarial search

2960-414: A pragmatic way. But for particularly difficult problems on the logical level, system 2 is employed. System 2 is mostly responsible for deductive reasoning. The ability of deductive reasoning is an important aspect of intelligence and many tests of intelligence include problems that call for deductive inferences. Because of this relation to intelligence, deduction is highly relevant to psychology and

3108-447: A rule of inference, are called formal fallacies . Rules of inference are definitory rules and contrast with strategic rules, which specify what inferences one needs to draw in order to arrive at an intended conclusion. Deductive reasoning contrasts with non-deductive or ampliative reasoning. For ampliative arguments, such as inductive or abductive arguments , the premises offer weaker support to their conclusion: they indicate that it

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3256-433: A set of premises, they are faced with the problem of choosing the relevant rules of inference for their deduction to arrive at their intended conclusion. This issue belongs to the field of strategic rules: the question of which inferences need to be drawn to support one's conclusion. The distinction between definitory and strategic rules is not exclusive to logic: it is also found in various games. In chess , for example,

3404-522: A special mechanism for permissions and obligations, specifically for detecting cheating in social exchanges. This can be used to explain why humans are often more successful in drawing valid inferences if the contents involve human behavior in relation to social norms. Another example is the so-called dual-process theory . This theory posits that there are two distinct cognitive systems responsible for reasoning. Their interrelation can be used to explain commonly observed biases in deductive reasoning. System 1

3552-719: A tool that can be used for reasoning (using the Bayesian inference algorithm), learning (using the expectation–maximization algorithm ), planning (using decision networks ) and perception (using dynamic Bayesian networks ). Probabilistic algorithms can also be used for filtering, prediction, smoothing, and finding explanations for streams of data, thus helping perception systems analyze processes that occur over time (e.g., hidden Markov models or Kalman filters ). The simplest AI applications can be divided into two types: classifiers (e.g., "if shiny then diamond"), on one hand, and controllers (e.g., "if diamond then pick up"), on

3700-413: A true conclusion given the premises are true. Some theorists hold that the thinker has to have explicit awareness of the truth-preserving nature of the inference for the justification to be transferred from the premises to the conclusion. One consequence of such a view is that, for young children, this deductive transference does not take place since they lack this specific awareness. Probability logic

3848-427: A universal account of deduction for language as an all-encompassing medium. Deductive reasoning usually happens by applying rules of inference . A rule of inference is a way or schema of drawing a conclusion from a set of premises. This happens usually based only on the logical form of the premises. A rule of inference is valid if, when applied to true premises, the conclusion cannot be false. A particular argument

3996-661: A wide range of techniques, including search and mathematical optimization , formal logic , artificial neural networks , and methods based on statistics , operations research , and economics . AI also draws upon psychology , linguistics , philosophy , neuroscience , and other fields. Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism, followed by periods of disappointment and loss of funding, known as AI winter . Funding and interest vastly increased after 2012 when deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with

4144-487: A wide variety of techniques to accomplish the goals above. AI can solve many problems by intelligently searching through many possible solutions. There are two very different kinds of search used in AI: state space search and local search . State space search searches through a tree of possible states to try to find a goal state. For example, planning algorithms search through trees of goals and subgoals, attempting to find

4292-403: Is affirming the consequent , as in "if John is a bachelor, then he is male; John is male; therefore, John is a bachelor". This is similar to the valid rule of inference named modus ponens , but the second premise and the conclusion are switched around, which is why it is invalid. A similar formal fallacy is denying the antecedent , as in "if Othello is a bachelor, then he is male; Othello is not

4440-455: Is valid if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises are true. An argument can be “valid” even if one or more of its premises are false. An argument is sound if it is valid and the premises are true. It is possible to have a deductive argument that is logically valid but is not sound . Fallacious arguments often take that form. The following

4588-635: Is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects; situations, events, states, and time; causes and effects; knowledge about knowledge (what we know about what other people know); default reasoning (things that humans assume are true until they are told differently and will remain true even when other facts are changing); and many other aspects and domains of knowledge. Among

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4736-537: Is a proposition whereas in Aristotelian logic, this common element is a term and not a proposition. The following is an example of an argument using a hypothetical syllogism: Various formal fallacies have been described. They are invalid forms of deductive reasoning. An additional aspect of them is that they appear to be valid on some occasions or on the first impression. They may thereby seduce people into accepting and committing them. One type of formal fallacy

4884-399: Is a quarterback" – are often used to make unsound arguments. The fact that there are some people who eat carrots but are not quarterbacks proves the flaw of the argument. In this example, the first statement uses categorical reasoning , saying that all carrot-eaters are definitely quarterbacks. This theory of deductive reasoning – also known as term logic – was developed by Aristotle , but

5032-408: Is a type of proof system based on simple and self-evident rules of inference. In philosophy, the geometrical method is a way of philosophizing that starts from a small set of self-evident axioms and tries to build a comprehensive logical system using deductive reasoning. Deductive reasoning is the psychological process of drawing deductive inferences . An inference is a set of premises together with

5180-435: Is an example of an argument that is “valid”, but not “sound”: The example's first premise is false – there are people who eat carrots who are not quarterbacks – but the conclusion would necessarily be true, if the premises were true. In other words, it is impossible for the premises to be true and the conclusion false. Therefore, the argument is “valid”, but not “sound”. False generalizations – such as "Everyone who eats carrots

5328-461: Is an interdisciplinary umbrella that comprises systems that recognize, interpret, process, or simulate human feeling, emotion, and mood . For example, some virtual assistants are programmed to speak conversationally or even to banter humorously; it makes them appear more sensitive to the emotional dynamics of human interaction, or to otherwise facilitate human–computer interaction . However, this tends to give naïve users an unrealistic conception of

5476-438: Is an unsolved problem. Knowledge representation and knowledge engineering allow AI programs to answer questions intelligently and make deductions about real-world facts. Formal knowledge representations are used in content-based indexing and retrieval, scene interpretation, clinical decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases ), and other areas. A knowledge base

5624-419: Is anything that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen. In automated planning , the agent has a specific goal. In automated decision-making , the agent has preferences—there are some situations it would prefer to be in, and some situations it is trying to avoid. The decision-making agent assigns a number to each situation (called

5772-574: Is called artificial intelligence . The word intelligence derives from the Latin nouns intelligentia or intellēctus , which in turn stem from the verb intelligere , to comprehend or perceive. In the Middle Ages , the word intellectus became the scholarly technical term for understanding and a translation for the Greek philosophical term nous . This term, however, was strongly linked to

5920-409: Is classified based on previous experience. There are many kinds of classifiers in use. The decision tree is the simplest and most widely used symbolic machine learning algorithm. K-nearest neighbor algorithm was the most widely used analogical AI until the mid-1990s, and Kernel methods such as the support vector machine (SVM) displaced k-nearest neighbor in the 1990s. The naive Bayes classifier

6068-415: Is deductive depends on the psychological state of the person making the argument: "An argument is deductive if, and only if, the author of the argument believes that the truth of the premises necessitates (guarantees) the truth of the conclusion". A similar formulation holds that the speaker claims or intends that the premises offer deductive support for their conclusion. This is sometimes categorized as

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6216-450: Is different from learning . Learning refers to the act of retaining facts and information or abilities and being able to recall them for future use. Intelligence, on the other hand, is the cognitive ability of someone to perform these and other processes. There have been various attempts to quantify intelligence via psychometric testing. Prominent among these are the various Intelligence Quotient (IQ) tests, which were first developed in

6364-425: Is difficult to apply to concrete cases since the intentions of the author are usually not explicitly stated. Deductive reasoning is studied in logic , psychology , and the cognitive sciences . Some theorists emphasize in their definition the difference between these fields. On this view, psychology studies deductive reasoning as an empirical mental process, i.e. what happens when humans engage in reasoning. But

6512-432: Is good if the author's belief concerning the relation between the premises and the conclusion is true, otherwise it is bad. One consequence of this approach is that deductive arguments cannot be identified by the law of inference they use. For example, an argument of the form modus ponens may be non-deductive if the author's beliefs are sufficiently confused. That brings with it an important drawback of this definition: it

6660-409: Is important to our mental health and has ties to social intelligence. Social intelligence is the ability to understand the social cues and motivations of others and oneself in social situations. It is thought to be distinct to other types of intelligence, but has relations to emotional intelligence. Social intelligence has coincided with other studies that focus on how we make judgements of others,

6808-468: Is interested in how the probability of the premises of an argument affects the probability of its conclusion. It differs from classical logic, which assumes that propositions are either true or false but does not take into consideration the probability or certainty that a proposition is true or false. Aristotle , a Greek philosopher , started documenting deductive reasoning in the 4th century BC. René Descartes , in his book Discourse on Method , refined

6956-412: Is labelled by a solution of the problem and whose leaf nodes are labelled by premises or axioms . In the case of Horn clauses , problem-solving search can be performed by reasoning forwards from the premises or backwards from the problem. In the more general case of the clausal form of first-order logic , resolution is a single, axiom-free rule of inference, in which a problem is solved by proving

7104-785: Is measured using a variety of interactive and observational tools focusing on innovation , habit reversal, social learning , and responses to novelty . Studies have shown that g is responsible for 47% of the individual variance in cognitive ability measures in primates and between 55% and 60% of the variance in mice (Locurto, Locurto). These values are similar to the accepted variance in IQ explained by g in humans (40–50%). It has been argued that plants should also be classified as intelligent based on their ability to sense and model external and internal environments and adjust their morphology , physiology and phenotype accordingly to ensure self-preservation and reproduction. A counter argument

7252-447: Is most likely, but they do not guarantee its truth. They make up for this drawback with their ability to provide genuinely new information (that is, information not already found in the premises), unlike deductive arguments. Cognitive psychology investigates the mental processes responsible for deductive reasoning. One of its topics concerns the factors determining whether people draw valid or invalid deductive inferences. One such factor

7400-413: Is necessary, formal, and knowable a priori . It is necessary in the sense that the premises of valid deductive arguments necessitate the conclusion: it is impossible for the premises to be true and the conclusion to be false, independent of any other circumstances. Logical consequence is formal in the sense that it depends only on the form or the syntax of the premises and the conclusion. This means that

7548-409: Is no possible interpretation of the argument whereby its premises are true and its conclusion is false. The syntactic approach, by contrast, focuses on rules of inference , that is, schemas of drawing a conclusion from a set of premises based only on their logical form . There are various rules of inference, such as modus ponens and modus tollens . Invalid deductive arguments, which do not follow

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7696-495: Is not always precisely observed in the academic literature. One important aspect of this difference is that logic is not interested in whether the conclusion of an argument is sensible. So from the premise "the printer has ink" one may draw the unhelpful conclusion "the printer has ink and the printer has ink and the printer has ink", which has little relevance from a psychological point of view. Instead, actual reasoners usually try to remove redundant or irrelevant information and make

7844-403: Is often explained in terms of probability : the premises make it more likely that the conclusion is true. Strong ampliative arguments make their conclusion very likely, but not absolutely certain. An example of ampliative reasoning is the inference from the premise "every raven in a random sample of 3200 ravens is black" to the conclusion "all ravens are black": the extensive random sample makes

7992-406: Is often motivated by seeing deduction and induction as two inverse processes that complement each other: deduction is top-down while induction is bottom-up . But this is a misconception that does not reflect how valid deduction is defined in the field of logic : a deduction is valid if it is impossible for its premises to be true while its conclusion is false, independent of whether the premises or

8140-525: Is possible that their premises are true and their conclusion is false. Two important forms of ampliative reasoning are inductive and abductive reasoning . Sometimes the term "inductive reasoning" is used in a very wide sense to cover all forms of ampliative reasoning. However, in a more strict usage, inductive reasoning is just one form of ampliative reasoning. In the narrow sense, inductive inferences are forms of statistical generalization. They are usually based on many individual observations that all show

8288-474: Is relevant to various fields and issues. Epistemology tries to understand how justification is transferred from the belief in the premises to the belief in the conclusion in the process of deductive reasoning. Probability logic studies how the probability of the premises of an inference affects the probability of its conclusion. The controversial thesis of deductivism denies that there are other correct forms of inference besides deduction. Natural deduction

8436-478: Is reportedly the "most widely used learner" at Google, due in part to its scalability. Neural networks are also used as classifiers. An artificial neural network is based on a collection of nodes also known as artificial neurons , which loosely model the neurons in a biological brain. It is trained to recognise patterns; once trained, it can recognise those patterns in fresh data. There is an input, at least one hidden layer of nodes and an output. Each node applies

8584-457: Is sometimes defined as the "capacity to learn how to carry out a huge range of tasks". Mathematician Olle Häggström defines intelligence in terms of "optimization power", an agent's capacity for efficient cross-domain optimization of the world according to the agent's preferences, or more simply the ability to "steer the future into regions of possibility ranked high in a preference ordering". In this optimization framework, Deep Blue has

8732-402: Is sufficient. This is due to its truth-preserving nature: a theory can be falsified if one of its deductive consequences is false. So while inductive reasoning does not offer positive evidence for a theory, the theory still remains a viable competitor until falsified by empirical observation . In this sense, deduction alone is sufficient for discriminating between competing hypotheses about what

8880-788: Is that intelligence is commonly understood to involve the creation and use of persistent memories as opposed to computation that does not involve learning. If this is accepted as definitive of intelligence, then it includes the artificial intelligence of robots capable of "machine learning", but excludes those purely autonomic sense-reaction responses that can be observed in many plants. Plants are not limited to automated sensory-motor responses, however, they are capable of discriminating positive and negative experiences and of "learning" (registering memories) from their past experiences. They are also capable of communication, accurately computing their circumstances, using sophisticated cost–benefit analysis and taking tightly controlled actions to mitigate and control

9028-470: Is the problem of induction introduced by David Hume . It consists in the challenge of explaining how or whether inductive inferences based on past experiences support conclusions about future events. For example, a chicken comes to expect, based on all its past experiences, that the person entering its coop is going to feed it, until one day the person "at last wrings its neck instead". According to Karl Popper 's falsificationism, deductive reasoning alone

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9176-399: Is the cards D and 7. Many select card 3 instead, even though the conditional claim does not involve any requirements on what symbols can be found on the opposite side of card 3. But this result can be drastically changed if different symbols are used: the visible sides show "drinking a beer", "drinking a coke", "16 years of age", and "22 years of age" and the participants are asked to evaluate

9324-472: Is the case. Hypothetico-deductivism is a closely related scientific method, according to which science progresses by formulating hypotheses and then aims to falsify them by trying to make observations that run counter to their deductive consequences. The term " natural deduction " refers to a class of proof systems based on self-evident rules of inference. The first systems of natural deduction were developed by Gerhard Gentzen and Stanislaw Jaskowski in

9472-486: Is the following: The following is an example of an argument using modus tollens: A hypothetical syllogism is an inference that takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form: In there being a subformula in common between the two premises that does not occur in the consequence, this resembles syllogisms in term logic , although it differs in that this subformula

9620-534: Is the form of the argument: for example, people draw valid inferences more successfully for arguments of the form modus ponens than of the form modus tollens. Another factor is the content of the arguments: people are more likely to believe that an argument is valid if the claim made in its conclusion is plausible. A general finding is that people tend to perform better for realistic and concrete cases than for abstract cases. Psychological theories of deductive reasoning aim to explain these findings by providing an account of

9768-429: Is the older system in terms of evolution. It is based on associative learning and happens fast and automatically without demanding many cognitive resources. System 2, on the other hand, is of more recent evolutionary origin. It is slow and cognitively demanding, but also more flexible and under deliberate control. The dual-process theory posits that system 1 is the default system guiding most of our everyday reasoning in

9916-403: Is the process of proving a new statement ( conclusion ) from other statements that are given and assumed to be true (the premises ). Proofs can be structured as proof trees , in which nodes are labelled by sentences, and children nodes are connected to parent nodes by inference rules . Given a problem and a set of premises, problem-solving reduces to searching for a proof tree whose root node

10064-450: Is thought to be the ability to convey emotion to others in an understandable way as well as to read the emotions of others accurately. Some theories imply that a heightened emotional intelligence could also lead to faster generating and processing of emotions in addition to the accuracy. In addition, higher emotional intelligence is thought to help us manage emotions, which is beneficial for our problem-solving skills. Emotional intelligence

10212-556: Is uninformative on the depth level, in contrast to ampliative reasoning. But it may still be valuable on the surface level by presenting the information in the premises in a new and sometimes surprising way. A popular misconception of the relation between deduction and induction identifies their difference on the level of particular and general claims. On this view, deductive inferences start from general premises and draw particular conclusions, while inductive inferences start from particular premises and draw general conclusions. This idea

10360-438: Is used for game-playing programs, such as chess or Go. It searches through a tree of possible moves and counter-moves, looking for a winning position. Local search uses mathematical optimization to find a solution to a problem. It begins with some form of guess and refines it incrementally. Gradient descent is a type of local search that optimizes a set of numerical parameters by incrementally adjusting them to minimize

10508-452: Is used for reasoning and knowledge representation . Formal logic comes in two main forms: propositional logic (which operates on statements that are true or false and uses logical connectives such as "and", "or", "not" and "implies") and predicate logic (which also operates on objects, predicates and relations and uses quantifiers such as " Every X is a Y " and "There are some X s that are Y s"). Deductive reasoning in logic

10656-432: Is used in AI programs that make decisions that involve other agents. Machine learning is the study of programs that can improve their performance on a given task automatically. It has been a part of AI from the beginning. There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns and makes predictions without any other guidance. Supervised learning requires labeling

10804-476: Is usually contrasted with non-deductive or ampliative reasoning. The hallmark of valid deductive inferences is that it is impossible for their premises to be true and their conclusion to be false. In this way, the premises provide the strongest possible support to their conclusion. The premises of ampliative inferences also support their conclusion. But this support is weaker: they are not necessarily truth-preserving. So even for correct ampliative arguments, it

10952-604: Is valid if and only if, there is no possible world in which its conclusion is false while its premises are true. This means that there are no counterexamples: the conclusion is true in all such cases, not just in most cases. It has been argued against this and similar definitions that they fail to distinguish between valid and invalid deductive reasoning, i.e. they leave it open whether there are invalid deductive inferences and how to define them. Some authors define deductive reasoning in psychological terms in order to avoid this problem. According to Mark Vorobey, whether an argument

11100-481: Is valid if it follows a valid rule of inference. Deductive arguments that do not follow a valid rule of inference are called formal fallacies : the truth of their premises does not ensure the truth of their conclusion. In some cases, whether a rule of inference is valid depends on the logical system one is using. The dominant logical system is classical logic and the rules of inference listed here are all valid in classical logic. But so-called deviant logics provide

11248-899: Is when the knowledge gained from one problem is applied to a new problem. Deep learning is a type of machine learning that runs inputs through biologically inspired artificial neural networks for all of these types of learning. Computational learning theory can assess learners by computational complexity , by sample complexity (how much data is required), or by other notions of optimization . Natural language processing (NLP) allows programs to read, write and communicate in human languages such as English . Specific problems include speech recognition , speech synthesis , machine translation , information extraction , information retrieval and question answering . Early work, based on Noam Chomsky 's generative grammar and semantic networks , had difficulty with word-sense disambiguation unless restricted to small domains called " micro-worlds " (due to

11396-594: The Wason selection task . In an often-cited experiment by Peter Wason , 4 cards are presented to the participant. In one case, the visible sides show the symbols D, K, 3, and 7 on the different cards. The participant is told that every card has a letter on one side and a number on the other side, and that "[e]very card which has a D on one side has a 3 on the other side". Their task is to identify which cards need to be turned around in order to confirm or refute this conditional claim. The correct answer, only given by about 10%,

11544-513: The bar exam , SAT test, GRE test, and many other real-world applications. Machine perception is the ability to use input from sensors (such as cameras, microphones, wireless signals, active lidar , sonar, radar, and tactile sensors ) to deduce aspects of the world. Computer vision is the ability to analyze visual input. The field includes speech recognition , image classification , facial recognition , object recognition , object tracking , and robotic perception . Affective computing

11692-659: The metaphysical and cosmological theories of teleological scholasticism , including theories of the immortality of the soul, and the concept of the active intellect (also known as the active intelligence). This approach to the study of nature was strongly rejected by early modern philosophers such as Francis Bacon , Thomas Hobbes , John Locke , and David Hume , all of whom preferred "understanding" (in place of " intellectus " or "intelligence") in their English philosophical works. Hobbes for example, in his Latin De Corpore , used " intellectus intelligit ", translated in

11840-463: The modus tollens , than with others, like the modus ponens : because the more error-prone forms do not have a native rule of inference but need to be calculated by combining several inferential steps with other rules of inference. In such cases, the additional cognitive labor makes the inferences more open to error. Mental model theories , on the other hand, hold that deductive reasoning involves models or mental representations of possible states of

11988-534: The quantifiers " ∃ {\displaystyle \exists } " and " ∀ {\displaystyle \forall } " . The focus on rules of inferences instead of axiom schemes is an important feature of natural deduction. But there is no general agreement on how natural deduction is to be defined. Some theorists hold that all proof systems with this feature are forms of natural deduction. This would include various forms of sequent calculi or tableau calculi . But other theorists use

12136-415: The transformer architecture , and by the early 2020s hundreds of billions of dollars were being invested in AI (known as the " AI boom "). The widespread use of AI in the 21st century exposed several unintended consequences and harms in the present and raised concerns about its risks and long-term effects in the future, prompting discussions about regulatory policies to ensure the safety and benefits of

12284-462: The validity of IQ tests as a measure of intelligence as a whole. There is debate about the heritability of IQ , that is, what proportion of differences in IQ test performance between individuals are explained by genetic or environmental factors. The scientific consensus is that genetics does not explain average differences in IQ test performance between racial groups. Emotional intelligence

12432-434: The " utility ") that measures how much the agent prefers it. For each possible action, it can calculate the " expected utility ": the utility of all possible outcomes of the action, weighted by the probability that the outcome will occur. It can then choose the action with the maximum expected utility. In classical planning , the agent knows exactly what the effect of any action will be. In most real-world problems, however,

12580-668: The 1930s. The core motivation was to give a simple presentation of deductive reasoning that closely mirrors how reasoning actually takes place. In this sense, natural deduction stands in contrast to other less intuitive proof systems, such as Hilbert-style deductive systems , which employ axiom schemes to express logical truths . Natural deduction, on the other hand, avoids axioms schemes by including many different rules of inference that can be used to formulate proofs. These rules of inference express how logical constants behave. They are often divided into introduction rules and elimination rules . Introduction rules specify under which conditions

12728-489: The English version as "the understanding understandeth", as a typical example of a logical absurdity . "Intelligence" has therefore become less common in English language philosophy, but it has later been taken up (with the scholastic theories that it now implies) in more contemporary psychology . There is controversy over how to define intelligence. Scholars describe its constituent abilities in various ways, and differ in

12876-429: The accuracy with which we do so, and why people would be viewed as having positive or negative social character . There is debate as to whether or not these studies and social intelligence come from the same theories or if there is a distinction between them, and they are generally thought to be of two different schools of thought . Moral intelligence is the capacity to understand right from wrong and to behave based on

13024-419: The agent can seek information to improve its preferences. Information value theory can be used to weigh the value of exploratory or experimental actions. The space of possible future actions and situations is typically intractably large, so the agents must take actions and evaluate situations while being uncertain of what the outcome will be. A Markov decision process has a transition model that describes

13172-509: The agent may not be certain about the situation they are in (it is "unknown" or "unobservable") and it may not know for certain what will happen after each possible action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning ), or

13320-522: The agent to operate with incomplete or uncertain information. AI researchers have devised a number of tools to solve these problems using methods from probability theory and economics. Precise mathematical tools have been developed that analyze how an agent can make choices and plan, using decision theory , decision analysis , and information value theory . These tools include models such as Markov decision processes , dynamic decision networks , game theory and mechanism design . Bayesian networks are

13468-419: The argument in a formal language in order to assess whether it is valid. This often brings with it the difficulty of translating the natural language argument into a formal language, a process that comes with various problems of its own. Another difficulty is due to the fact that the syntactic approach depends on the distinction between formal and non-formal features. While there is a wide agreement concerning

13616-406: The claim "[i]f a person is drinking beer, then the person must be over 19 years of age". In this case, 74% of the participants identified correctly that the cards "drinking a beer" and "16 years of age" have to be turned around. These findings suggest that the deductive reasoning ability is heavily influenced by the content of the involved claims and not just by the abstract logical form of the task:

13764-533: The cognitive abilities to learn , form concepts , understand , and reason , including the capacities to recognize patterns , innovate, plan , solve problems , and employ language to communicate . These cognitive abilities can be organized into frameworks like fluid vs. crystallized and the Unified Cattell-Horn-Carroll model, which contains abilities like fluid reasoning, perceptual speed, verbal abilities, and others. Intelligence

13912-418: The cognitive sciences. But the subject of deductive reasoning is also pertinent to the computer sciences , for example, in the creation of artificial intelligence . Deductive reasoning plays an important role in epistemology . Epistemology is concerned with the question of justification , i.e. to point out which beliefs are justified and why. Deductive inferences are able to transfer the justification of

14060-642: The common sense knowledge problem). Margaret Masterman believed that it was meaning and not grammar that was the key to understanding languages, and that thesauri and not dictionaries should be the basis of computational language structure. Modern deep learning techniques for NLP include word embedding (representing words, typically as vectors encoding their meaning), transformers (a deep learning architecture using an attention mechanism), and others. In 2019, generative pre-trained transformer (or "GPT") language models began to generate coherent text, and by 2023, these models were able to get human-level scores on

14208-408: The common syntax explicit. There are various other valid logical forms or rules of inference , like modus tollens or the disjunction elimination . The syntactic approach then holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference. One difficulty for the syntactic approach is that it is usually necessary to express

14356-490: The conclusion " A ∧ B {\displaystyle A\land B} " and thereby include it in one's proof. This way, the symbol " ∧ {\displaystyle \land } " is introduced into the proof. The removal of this symbol is governed by other rules of inference, such as the elimination rule " ( A ∧ B ) A {\displaystyle {\frac {(A\land B)}{A}}} " , which states that one may deduce

14504-467: The conclusion are particular or general. Because of this, some deductive inferences have a general conclusion and some also have particular premises. Cognitive psychology studies the psychological processes responsible for deductive reasoning. It is concerned, among other things, with how good people are at drawing valid deductive inferences. This includes the study of the factors affecting their performance, their tendency to commit fallacies , and

14652-528: The conclusion is true because its two premises are true. But even arguments with wrong premises can be deductively valid if they obey this principle, as in "all frogs are mammals; no cats are mammals; therefore, no cats are frogs". If the premises of a valid argument are true, then it is called a sound argument. The relation between the premises and the conclusion of a deductive argument is usually referred to as " logical consequence ". According to Alfred Tarski , logical consequence has 3 essential features: it

14800-513: The conclusion only repeats information already found in the premises. Ampliative reasoning, on the other hand, goes beyond the premises by arriving at genuinely new information. One difficulty for this characterization is that it makes deductive reasoning appear useless: if deduction is uninformative, it is not clear why people would engage in it and study it. It has been suggested that this problem can be solved by distinguishing between surface and depth information. On this view, deductive reasoning

14948-433: The conclusion very likely, but it does not exclude that there are rare exceptions. In this sense, ampliative reasoning is defeasible: it may become necessary to retract an earlier conclusion upon receiving new related information. Ampliative reasoning is very common in everyday discourse and the sciences . An important drawback of deductive reasoning is that it does not lead to genuinely new information. This means that

15096-402: The consequent or denying the antecedent were regarded as valid arguments by the majority of the subjects. An important factor for these mistakes is whether the conclusion seems initially plausible: the more believable the conclusion is, the higher the chance that a subject will mistake a fallacy for a valid argument. An important bias is the matching bias , which is often illustrated using

15244-404: The consequent ( Q {\displaystyle Q} ) obtains as the conclusion from the premises of a conditional statement ( P → Q {\displaystyle P\rightarrow Q} ) and its antecedent ( P {\displaystyle P} ). However, the antecedent ( P {\displaystyle P} ) cannot be similarly obtained as the conclusion from

15392-581: The content rather than the form of the argument. For example, when the conclusion of an argument is very plausible, the subjects may lack the motivation to search for counterexamples among the constructed models. Both mental logic theories and mental model theories assume that there is one general-purpose reasoning mechanism that applies to all forms of deductive reasoning. But there are also alternative accounts that posit various different special-purpose reasoning mechanisms for different contents and contexts. In this sense, it has been claimed that humans possess

15540-576: The definitory rules state that bishops may only move diagonally while the strategic rules recommend that one should control the center and protect one's king if one intends to win. In this sense, definitory rules determine whether one plays chess or something else whereas strategic rules determine whether one is a good or a bad chess player. The same applies to deductive reasoning: to be an effective reasoner involves mastering both definitory and strategic rules. Deductive arguments are evaluated in terms of their validity and soundness . An argument

15688-709: The degree to which they conceive of intelligence as quantifiable. A consensus report called Intelligence: Knowns and Unknowns , published in 1995 by the Board of Scientific Affairs of the American Psychological Association , states: Individuals differ from one another in their ability to understand complex ideas, to adapt effectively to the environment, to learn from experience, to engage in various forms of reasoning, to overcome obstacles by taking thought. Although these individual differences can be substantial, they are never entirely consistent:

15836-425: The descriptive question of how actual reasoning happens is different from the normative question of how it should happen or what constitutes correct deductive reasoning, which is studied by logic. This is sometimes expressed by stating that, strictly speaking, logic does not study deductive reasoning but the deductive relation between premises and a conclusion known as logical consequence . But this distinction

15984-870: The diverse environmental stressors. Scholars studying artificial intelligence have proposed definitions of intelligence that include the intelligence demonstrated by machines. Some of these definitions are meant to be general enough to encompass human and other animal intelligence as well. An intelligent agent can be defined as a system that perceives its environment and takes actions which maximize its chances of success. Kaplan and Haenlein define artificial intelligence as "a system's ability to correctly interpret external data, to learn from such data, and to use those learnings to achieve specific goals and tasks through flexible adaptation". Progress in artificial intelligence can be demonstrated in benchmarks ranging from games to practical tasks such as protein folding . Existing AI lags humans in terms of general intelligence, which

16132-431: The early 1900s. Most psychologists believe that intelligence can be divided into various domains or competencies. Intelligence has been long-studied in humans , and across numerous disciplines. It has also been observed in the cognition of non-human animals . Some researchers have suggested that plants exhibit forms of intelligence, though this remains controversial. Intelligence in computers or other machines

16280-400: The early 20th century to screen children for intellectual disability . Over time, IQ tests became more pervasive, being used to screen immigrants, military recruits, and job applicants. As the tests became more popular, belief that IQ tests measure a fundamental and unchanging attribute that all humans possess became widespread. An influential theory that promoted the idea that IQ measures

16428-449: The expressions used in the sentences, such as the reference to an object for singular terms or to a truth-value for atomic sentences. The semantic approach is also referred to as the model-theoretic approach since the branch of mathematics known as model theory is often used to interpret these sentences. Usually, many different interpretations are possible, such as whether a singular term refers to one object or to another. According to

16576-617: The following: "Intelligence is a force, F, that acts so as to maximize future freedom of action. It acts to maximize future freedom of action, or keep options open, with some strength T, with the diversity of possible accessible futures, S, up to some future time horizon, τ. In short, intelligence doesn't like to get trapped". Human intelligence is the intellectual power of humans, which is marked by complex cognitive feats and high levels of motivation and self-awareness . Intelligence enables humans to remember descriptions of things and use those descriptions in future behaviors. It gives humans

16724-475: The foundations for the ideas of rationalism . Deductivism is a philosophical position that gives primacy to deductive reasoning or arguments over their non-deductive counterparts. It is often understood as the evaluative claim that only deductive inferences are good or correct inferences. This theory would have wide-reaching consequences for various fields since it implies that the rules of deduction are "the only acceptable standard of evidence ". This way,

16872-620: The idea for the Scientific Revolution . Developing four rules to follow for proving an idea deductively, Descartes laid the foundation for the deductive portion of the scientific method . Descartes' background in geometry and mathematics influenced his ideas on the truth and reasoning, causing him to develop a system of general reasoning now used for most mathematical reasoning. Similar to postulates, Descartes believed that ideas could be self-evident and that reasoning alone must prove that observations are reliable. These ideas also lay

17020-423: The importance of learning through text in our own personal lives and in our culture, it is perhaps surprising how utterly dismissive we tend to be of it. It is sometimes derided as being merely "book knowledge", and having it is being "book smart". In contrast, knowledge acquired through direct experience and apprenticeship is called "street knowledge", and having it is being "street smart". Although humans have been

17168-437: The intelligence of existing computer agents. Moderate successes related to affective computing include textual sentiment analysis and, more recently, multimodal sentiment analysis , wherein AI classifies the affects displayed by a videotaped subject. A machine with artificial general intelligence should be able to solve a wide variety of problems with breadth and versatility similar to human intelligence . AI research uses

17316-424: The language-using Kanzi ) and other great apes , dolphins , elephants and to some extent parrots , rats and ravens . Cephalopod intelligence provides an important comparative study. Cephalopods appear to exhibit characteristics of significant intelligence, yet their nervous systems differ radically from those of backboned animals. Vertebrates such as mammals , birds , reptiles and fish have shown

17464-534: The late 1980s and 1990s, methods were developed for dealing with uncertain or incomplete information, employing concepts from probability and economics . Many of these algorithms are insufficient for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans rarely use the step-by-step deduction that early AI research could model. They solve most of their problems using fast, intuitive judgments. Accurate and efficient reasoning

17612-414: The manipulation of representations. This is done by applying syntactic rules of inference in a way very similar to how systems of natural deduction transform their premises to arrive at a conclusion. On this view, some deductions are simpler than others since they involve fewer inferential steps. This idea can be used, for example, to explain why humans have more difficulties with some deductions, like

17760-439: The more realistic and concrete the cases are, the better the subjects tend to perform. Another bias is called the "negative conclusion bias", which happens when one of the premises has the form of a negative material conditional , as in "If the card does not have an A on the left, then it has a 3 on the right. The card does not have a 3 on the right. Therefore, the card has an A on the left". The increased tendency to misjudge

17908-454: The most difficult problems in knowledge representation are the breadth of commonsense knowledge (the set of atomic facts that the average person knows is enormous); and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they could express verbally). There is also the difficulty of knowledge acquisition , the problem of obtaining knowledge for AI applications. An "agent"

18056-404: The other hand. Classifiers are functions that use pattern matching to determine the closest match. They can be fine-tuned based on chosen examples using supervised learning . Each pattern (also called an " observation ") is labeled with a certain predefined class. All the observations combined with their class labels are known as a data set . When a new observation is received, that observation

18204-423: The paradigmatic cases, there are also various controversial cases where it is not clear how this distinction is to be drawn. The semantic approach suggests an alternative definition of deductive validity. It is based on the idea that the sentences constituting the premises and conclusions have to be interpreted in order to determine whether the argument is valid. This means that one ascribes semantic values to

18352-431: The power to "steer a chessboard's future into a subspace of possibility which it labels as 'winning', despite attempts by Garry Kasparov to steer the future elsewhere." Hutter and Legg , after surveying the literature, define intelligence as "an agent's ability to achieve goals in a wide range of environments". While cognitive ability is sometimes measured as a one-dimensional parameter, it could also be represented as

18500-404: The premises are true. Because of this, the evaluation of some forms of inference only requires the construction of very few models while for others, many different models are necessary. In the latter case, the additional cognitive labor required makes deductive reasoning more error-prone, thereby explaining the increased rate of error observed. This theory can also explain why some errors depend on

18648-471: The premises of the conditional statement ( P → Q {\displaystyle P\rightarrow Q} ) and the consequent ( Q {\displaystyle Q} ). Such an argument commits the logical fallacy of affirming the consequent . The following is an example of an argument using modus ponens: Modus tollens (also known as "the law of contrapositive") is a deductive rule of inference. It validates an argument that has as premises

18796-415: The premises onto the conclusion. So while logic is interested in the truth-preserving nature of deduction, epistemology is interested in the justification-preserving nature of deduction. There are different theories trying to explain why deductive reasoning is justification-preserving. According to reliabilism , this is the case because deductions are truth-preserving: they are reliable processes that ensure

18944-438: The primary focus of intelligence researchers, scientists have also attempted to investigate animal intelligence, or more broadly, animal cognition. These researchers are interested in studying both mental ability in a particular species , and comparing abilities between species. They study various measures of problem solving, as well as numerical and verbal reasoning abilities. Some challenges include defining intelligence so it has

19092-410: The probability that a particular action will change the state in a particular way and a reward function that supplies the utility of each state and the cost of each action. A policy associates a decision with each possible state. The policy could be calculated (e.g., by iteration ), be heuristic , or it can be learned. Game theory describes the rational behavior of multiple interacting agents and

19240-546: The rationality or correctness of the different forms of inductive reasoning is denied. Some forms of deductivism express this in terms of degrees of reasonableness or probability. Inductive inferences are usually seen as providing a certain degree of support for their conclusion: they make it more likely that their conclusion is true. Deductivism states that such inferences are not rational: the premises either ensure their conclusion, as in deductive reasoning, or they do not provide any support at all. One motivation for deductivism

19388-406: The relevant information more explicit. The psychological study of deductive reasoning is also concerned with how good people are at drawing deductive inferences and with the factors determining their performance. Deductive inferences are found both in natural language and in formal logical systems , such as propositional logic . Deductive arguments differ from non-deductive arguments in that

19536-424: The same arrangement, even if their contents differ. For example, the arguments "if it rains then the street will be wet; it rains; therefore, the street will be wet" and "if the meat is not cooled then it will spoil; the meat is not cooled; therefore, it will spoil" have the same logical form: they follow the modus ponens . Their form can be expressed more abstractly as "if A then B; A; therefore B" in order to make

19684-407: The same meaning across species, and operationalizing a measure that accurately compares mental ability across species and contexts. Wolfgang Köhler 's research on the intelligence of apes is an example of research in this area, as is Stanley Coren's book, The Intelligence of Dogs . Non-human animals particularly noted and studied for their intelligence include chimpanzees , bonobos (notably

19832-412: The semantic approach, an argument is deductively valid if and only if there is no possible interpretation where its premises are true and its conclusion is false. Some objections to the semantic approach are based on the claim that the semantics of a language cannot be expressed in the same language, i.e. that a richer metalanguage is necessary. This would imply that the semantic approach cannot provide

19980-520: The sentence " A {\displaystyle A} " from the premise " ( A ∧ B ) {\displaystyle (A\land B)} " . Similar introduction and elimination rules are given for other logical constants, such as the propositional operator " ¬ {\displaystyle \lnot } " , the propositional connectives " ∨ {\displaystyle \lor } " and " → {\displaystyle \rightarrow } " , and

20128-469: The technology . The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research. Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions . By

20276-449: The training data with the expected answers, and comes in two main varieties: classification (where the program must learn to predict what category the input belongs in) and regression (where the program must deduce a numeric function based on numeric input). In reinforcement learning , the agent is rewarded for good responses and punished for bad ones. The agent learns to choose responses that are classified as "good". Transfer learning

20424-435: The truth of their conclusion. But it may still happen by coincidence that both the premises and the conclusion of formal fallacies are true. Rules of inferences are definitory rules: they determine whether an argument is deductively valid or not. But reasoners are usually not just interested in making any kind of valid argument. Instead, they often have a specific point or conclusion that they wish to prove or refute. So given

20572-407: The truth of their premises ensures the truth of their conclusion. There are two important conceptions of what this exactly means. They are referred to as the syntactic and the semantic approach. According to the syntactic approach, whether an argument is deductively valid depends only on its form, syntax, or structure. Two arguments have the same form if they use the same logical vocabulary in

20720-406: The underlying biases involved. A notable finding in this field is that the type of deductive inference has a significant impact on whether the correct conclusion is drawn. In a meta-analysis of 65 studies, for example, 97% of the subjects evaluated modus ponens inferences correctly, while the success rate for modus tollens was only 72%. On the other hand, even some fallacies like affirming

20868-438: The underlying psychological processes responsible. They are often used to explain the empirical findings, such as why human reasoners are more susceptible to some types of fallacies than to others. An important distinction is between mental logic theories , sometimes also referred to as rule theories , and mental model theories . Mental logic theories see deductive reasoning as a language -like process that happens through

21016-543: The underlying psychological processes. Mental logic theories hold that deductive reasoning is a language-like process that happens through the manipulation of representations using rules of inference. Mental model theories , on the other hand, claim that deductive reasoning involves models of possible states of the world without the medium of language or rules of inference. According to dual-process theories of reasoning, there are two qualitatively different cognitive systems responsible for reasoning. The problem of deduction

21164-418: The use of particular tools. The traditional goals of AI research include reasoning , knowledge representation , planning , learning , natural language processing , perception, and support for robotics . General intelligence —the ability to complete any task performable by a human on an at least equal level—is among the field's long-term goals. To reach these goals, AI researchers have adapted and integrated

21312-547: The validity of a particular argument does not depend on the specific contents of this argument. If it is valid, then any argument with the same logical form is also valid, no matter how different it is on the level of its contents. Logical consequence is knowable a priori in the sense that no empirical knowledge of the world is necessary to determine whether a deduction is valid. So it is not necessary to engage in any form of empirical investigation. Some logicians define deduction in terms of possible worlds : A deductive inference

21460-405: The validity of this type of argument is not present for positive material conditionals, as in "If the card has an A on the left, then it has a 3 on the right. The card does not have a 3 on the right. Therefore, the card does not have an A on the left". Various psychological theories of deductive reasoning have been proposed. These theories aim to explain how deductive reasoning works in relation to

21608-617: The value that is believed to be right. It is considered a distinct form of intelligence, independent to both emotional and cognitive intelligence. Concepts of "book smarts" and "street smart" are contrasting views based on the premise that some people have knowledge gained through academic study, but may lack the experience to sensibly apply that knowledge, while others have knowledge gained through practical experience, but may lack accurate information usually gained through study by which to effectively apply that knowledge. Artificial intelligence researcher Hector Levesque has noted that: Given

21756-492: The world without the medium of language or rules of inference. In order to assess whether a deductive inference is valid, the reasoner mentally constructs models that are compatible with the premises of the inference. The conclusion is then tested by looking at these models and trying to find a counterexample in which the conclusion is false. The inference is valid if no such counterexample can be found. In order to reduce cognitive labor, only such models are represented in which

21904-410: Was superseded by propositional (sentential) logic and predicate logic . Deductive reasoning can be contrasted with inductive reasoning , in regards to validity and soundness. In cases of inductive reasoning, even though the premises are true and the argument is “valid”, it is possible for the conclusion to be false (determined to be false with a counterexample or other means). Deductive reasoning

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