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49-504: Progol is an implementation of inductive logic programming that combines inverse entailment with general-to-specific search through a refinement graph . Inverse entailment is used with mode declarations to derive the bottom clause, the most-specific clause within the mode language which subsume a given example. This clause is used to guide a refinement-graph search. Unlike the searches of Ehud Shapiro 's model inference system (MIS) and J. Ross Quinlan 's FOIL , Progol's search has

98-470: A d ← b o d y {\textstyle \mathrm {head} \leftarrow \mathrm {body} } in B ∪ H {\textstyle B\cup H} such that b o d y θ ⊆ e {\textstyle \mathrm {body} \theta \subseteq e} , h e a d θ ⊆ e {\displaystyle \mathrm {head} \theta \subseteq e} also holds. The goal

147-583: A background theory. In general, such relative least general generalisations are not guaranteed to exist; however, if the background theory B is a finite set of ground literals , then the negation of B is itself a clause. In this case, a relative least general generalisation can be computed by disjoining the negation of B with both C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} and then computing their least general generalisation as before. Relative least general generalisations are

196-464: A beam search among probabilistic logic programs by iteratively refining probabilistic theories and optimizing the parameters of each theory using expectation-maximisation. Its extension SLIPCOVER, proposed in 2014, uses bottom clauses generated as in Progol to guide the refinement process, thus reducing the number of revisions and exploring the search space more effectively. Moreover, SLIPCOVER separates

245-439: A bridge theory satisfying the conditions B ∧ ¬ E ⊨ F {\displaystyle B\land \neg E\models F} and F ⊨ ¬ H {\displaystyle F\models \neg H} . Then as H ⊨ ¬ F {\displaystyle H\models \neg F} , they generalize the negation of the bridge theory F with anti-entailment. However,

294-694: A clause C 2 {\textstyle C_{2}} such that R {\textstyle R} is the resolvent of C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} . A W-operator takes two clauses R 1 {\textstyle R_{1}} and R 2 {\textstyle R_{2}} and returns thre clauses C 1 {\textstyle C_{1}} , C 2 {\textstyle C_{2}} and C 3 {\textstyle C_{3}} such that R 1 {\textstyle R_{1}}

343-744: A clause C {\textstyle C} that subsumes C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} , and that is subsumed by every other clause that subsumes C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} . The least general generalisation can be computed by first computing all selections from C {\textstyle C} and D {\textstyle D} , which are pairs of literals ( L , M ) ∈ ( C 1 , C 2 ) {\displaystyle (L,M)\in (C_{1},C_{2})} sharing

392-614: A correct hypothesis H with respect to theories B , E + , E − {\displaystyle B,E^{+},E^{-}} . A system is complete if and only if for any input logic theories B , E + , E − {\displaystyle B,E^{+},E^{-}} any correct hypothesis H with respect to these input theories can be found with its hypothesis search procedure. Inductive logic programming systems can be roughly divided into two classes, search-based and meta-interpretative systems. Search-based systems exploit that

441-400: A form of statistical relational learning within the formalism of probabilistic logic programming. Given the goal of probabilistic inductive logic programming is to find a probabilistic logic program H {\textstyle H} such that the probability of positive examples according to H ∪ B {\textstyle {H\cup B}} is maximized and

490-473: A meta-level logic program which is then solved to obtain an optimal hypothesis. Formalisms used to express the problem specification include Prolog and answer set programming , with existing Prolog systems and answer set solvers used for solving the constraints. And example of a Prolog-based system is Metagol , which is based on a meta-interpreter in Prolog , while ASPAL and ILASP are based on an encoding of

539-490: A paper by Stephen Muggleton in 1990, defined as the intersection of machine learning and logic programming. Muggleton and Wray Buntine introduced predicate invention and inverse resolution in 1988. Several inductive logic programming systems that proved influential appeared in the early 1990s. FOIL , introduced by Ross Quinlan in 1990 was based on upgrading propositional learning algorithms AQ and ID3 . Golem , introduced by Muggleton and Feng in 1990, went back to

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588-489: A provable guarantee of returning a solution having the maximum compression in the search-space. To do so it performs an admissible A* -like search, guided by compression, over clauses which subsume the most specific clause. Progol deals with noisy data by using a compression measure to trade off the description of errors against the hypothesis description length. Progol allows arbitrary Prolog programs as background knowledge and arbitrary definite clauses as examples. Progol

637-638: A restricted form of Plotkin's least generalisation algorithm. The Progol system, introduced by Muggleton in 1995, first implemented inverse entailment, and inspired many later systems. Aleph , a descendant of Progol introduced by Ashwin Srinivasan in 2001, is still one of the most widely used systems as of 2022 . At around the same time, the first practical applications emerged, particularly in bioinformatics , where by 2000 inductive logic programming had been successfully applied to drug design, carcinogenicity and mutagenicity prediction, and elucidation of

686-493: A restriction on h , but forbids any generation of a hypothesis as long as the positive facts are explainable without it. . "Weak consistency", which states that no contradiction can be derived from B ∧ H {\textstyle B\land H} , forbids generation of any hypothesis h that contradicts the background knowledge B . Weak consistency is implied by strong consistency; if no negative examples are given, both requirements coincide. Weak consistency

735-547: A sub-routine library, and sorting programs, our task was to look at the larger programming process. We needed to understand how we might reuse tested code and have the machine help in programming. As we programmed, we examined the process and tried to think of ways to abstract these steps to incorporate them into higher-level language. This led to the development of interpreters, assemblers, compilers, and generators—programs designed to operate on or produce other programs, that is, automatic programming ." Generative programming and

784-847: Is a set of clauses satisfying the following requirements, where the turnstile symbol ⊨ {\displaystyle \models } stands for logical entailment : Completeness: B ∪ H ⊨ E + Consistency:  B ∪ H ∪ E − ⊭ false {\displaystyle {\begin{array}{llll}{\text{Completeness:}}&B\cup H&\models &E^{+}\\{\text{Consistency: }}&B\cup H\cup E^{-}&\not \models &{\textit {false}}\end{array}}} Completeness requires any generated hypothesis h to explain all positive examples E + {\textstyle E^{+}} , and consistency forbids generation of any hypothesis h that

833-404: Is a type of computer programming in which some mechanism generates a computer program to allow human programmers to write the code at a higher abstraction level. There has been little agreement on the precise definition of automatic programming, mostly because its meaning has changed over time. David Parnas , tracing the history of "automatic programming" in published research, noted that in

882-576: Is given as a hypothesis H , itself a logical theory that typically consists of one or more clauses. The two settings differ in the format of examples presented. As of 2022 , learning from entailment is by far the most popular setting for inductive logic programming. In this setting, the positive and negative examples are given as finite sets E + {\textstyle E^{+}} and E − {\textstyle E^{-}} of positive and negated ground literals , respectively. A correct hypothesis H

931-464: Is inconsistent with the negative examples E − {\textstyle E^{-}} , both given the background knowledge B . In Muggleton's setting of concept learning, "completeness" is referred to as "sufficiency", and "consistency" as "strong consistency". Two further conditions are added: " Necessity ", which postulates that B does not entail E + {\textstyle E^{+}} , does not impose

980-573: Is particularly important in the case of noisy data, where completeness and strong consistency cannot be guaranteed. In learning from interpretations, the positive and negative examples are given as a set of complete or partial Herbrand structures , each of which are themselves a finite set of ground literals. Such a structure e is said to be a model of the set of clauses B ∪ H {\textstyle B\cup H} if for any substitution θ {\textstyle \theta } and any clause h e

1029-603: Is the process of generating source code based on a description of the problem or an ontological model such as a template and is accomplished with a programming tool such as a template processor or an integrated development environment (IDE). These tools allow the generation of source code through any of various means. Modern programming languages are well supported by tools like Json4Swift ( Swift ) and Json2Kotlin ( Kotlin ). Programs that could generate COBOL code include: These application generators supported COBOL inserts and overrides. A macro processor, such as

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1078-455: Is the resolvent of C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} and R 2 {\textstyle R_{2}} is the resolvent of C 2 {\textstyle C_{2}} and C 3 {\textstyle C_{3}} . Inverse resolution was first introduced by Stephen Muggleton and Wray Buntine in 1988 for use in

1127-513: Is then to output a hypothesis that is complete, meaning every positive example is a model of B ∪ H {\textstyle B\cup H} , and consistent, meaning that no negative example is a model of B ∪ H {\textstyle B\cup H} . An inductive logic programming system is a program that takes as an input logic theories B , E + , E − {\displaystyle B,E^{+},E^{-}} and outputs

1176-399: The C preprocessor , which replaces patterns in source code according to relatively simple rules, is a simple form of source-code generator. Source-to-source code generation tools also exist. Large language models such as ChatGPT are capable of generating a program's source code from a description of the program given in a natural language. Many relational database systems provide

1225-409: The resolution inference rule. A least general generalisation algorithm takes as input two clauses C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} and outputs the least general generalisation of C 1 {\textstyle C_{1}} and C 2 {\textstyle C_{2}} , that is,

1274-417: The 1940s it described automation of the manual process of punching paper tape . Later it referred to translation of high-level programming languages like Fortran and ALGOL . In fact, one of the earliest programs identifiable as a compiler was called Autocode . Parnas concluded that "automatic programming has always been a euphemism for programming in a higher-level language than was then available to

1323-452: The Progol hypothesis search procedure based on the inverse entailment inference rule is not complete by Yamamoto's example . On the other hand, Imparo is complete by both anti-entailment procedure and its extended inverse subsumption procedure. Rather than explicitly searching the hypothesis graph, metainterpretive or meta-level systems encode the inductive logic programming program as

1372-444: The authors learn the structure of first-order rules with associated probabilistic uncertainty parameters. Their approach involves generating the underlying graphical model in a preliminary step and then applying expectation-maximisation. In 2008, De Raedt et al. presented an algorithm for performing theory compression on ProbLog programs, where theory compression refers to a process of removing as many clauses as possible from

1421-417: The examples can be given as examples or as (partial) interpretations. Parameter learning for languages following the distribution semantics has been performed by using an expectation-maximisation algorithm or by gradient descent . An expectation-maximisation algorithm consists of a cycle in which the steps of expectation and maximization are repeatedly performed. In the expectation step, the distribution of

1470-478: The field in his new approach of model inference, an algorithm employing refinement and backtracing to search for a complete axiomatisation of given examples. His first implementation was the Model Inference System in 1981: a Prolog program that inductively inferred Horn clause logic programs from positive and negative examples. The term Inductive Logic Programming was first introduced in

1519-510: The field, and the widely-used inductive logic programming system Aleph builds directly on Progol. Inductive logic programming Inductive logic programming is particularly useful in bioinformatics and natural language processing . Building on earlier work on Inductive inference , Gordon Plotkin was the first to formalise induction in a clausal setting around 1970, adopting an approach of generalising from examples. In 1981, Ehud Shapiro introduced several ideas that would shape

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1568-549: The foundation of the bottom-up system Golem . Inverse resolution is an inductive reasoning technique that involves inverting the resolution operator . Inverse resolution takes information about the resolvent of a resolution step to compute possible resolving clauses. Two types of inverse resolution operator are in use in inductive logic programming: V-operators and W-operators. A V-operator takes clauses R {\textstyle R} and C 1 {\textstyle C_{1}} as input and returns

1617-411: The hidden variables is computed according to the current values of the probability parameters, while in the maximisation step, the new values of the parameters are computed. Gradient descent methods compute the gradient of the target function and iteratively modify the parameters moving in the direction of the gradient. Structure learning was pioneered by Daphne Koller and Avi Pfeffer in 1997, where

1666-549: The inductive logic programming problem in answer set programming. Evolutionary algorithms in ILP use a population-based approach to evolve hypotheses, refining them through selection, crossover, and mutation. Methods like EvoLearner have been shown to outperform traditional approaches on structured machine learning benchmarks. Probabilistic inductive logic programming adapts the setting of inductive logic programming to learning probabilistic logic programs . It can be considered as

1715-496: The inductive logic programming system FOIL with ProbLog . Logical rules are learned from probabilistic data in the sense that both the examples themselves and their classifications can be probabilistic. The set of rules has to allow one to predict the probability of the examples from their description. In this setting, the parameters (the probability values) are fixed and the structure has to be learned. In 2011, Elena Bellodi and Fabrizio Riguzzi introduced SLIPCASE, which performs

1764-561: The inductive logic programming system Cigol. By 1993, this spawned a surge of research into inverse resolution operators and their properties. The ILP systems Progol, Hail and Imparo find a hypothesis H using the principle of the inverse entailment for theories B , E , H : B ∧ H ⊨ E ⟺ B ∧ ¬ E ⊨ ¬ H {\displaystyle B\land H\models E\iff B\land \neg E\models \neg H} . First they construct an intermediate theory F called

1813-565: The introduction of meta-interpretative learning makes predicate invention and learning recursive programs more feasible. This technique was pioneered with the Metagol system introduced by Muggleton, Dianhuan Lin, Niels Pahlavi and Alireza Tamaddoni-Nezhad in 2014. This allows ILP systems to work with fewer examples, and brought successes in learning string transformation programs, answer set grammars and general algorithms. Inductive logic programming has adopted several different learning settings,

1862-461: The most common of which are learning from entailment and learning from interpretations. In both cases, the input is provided in the form of background knowledge B , a logical theory (commonly in the form of clauses used in logic programming ), as well as positive and negative examples, denoted E + {\textstyle E^{+}} and E − {\textstyle E^{-}} respectively. The output

1911-414: The operation of anti-entailment is computationally more expensive since it is highly nondeterministic. Therefore, an alternative hypothesis search can be conducted using the inverse subsumption (anti-subsumption) operation instead, which is less non-deterministic than anti-entailment. Questions of completeness of a hypothesis search procedure of specific inductive logic programming system arise. For example,

1960-416: The probability of negative examples is minimized. This problem has two variants: parameter learning and structure learning. In the former, one is given the structure (the clauses) of H and the goal is to infer the probabilities annotations of the given clauses, while in the latter the goal is to infer both the structure and the probability parameters of H . Just as in classical inductive logic programming,

2009-518: The programmer." Program synthesis is one type of automatic programming where a procedure is created from scratch, based on mathematical requirements. Mildred Koss , an early UNIVAC programmer, explains: "Writing machine code involved several tedious steps—breaking down a process into discrete instructions, assigning specific memory locations to all the commands, and managing the I/O buffers. After following these steps to implement mathematical routines,

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2058-440: The related term meta-programming are concepts whereby programs can be written "to manufacture software components in an automated way" just as automation has improved "production of traditional commodities such as garments, automobiles, chemicals, and electronics." The goal is to improve programmer productivity. It is often related to code-reuse topics such as component-based software engineering . Source-code generation

2107-562: The result of applying θ {\textstyle \theta } to C 1 {\textstyle C_{1}} , is a subset of C 2 {\textstyle C_{2}} . This lattice can be traversed either bottom-up or top-down. Bottom-up methods to search the subsumption lattice have been investigated since Plotkin's first work on formalising induction in clausal logic in 1970. Techniques used include least general generalisation, based on anti-unification , and inverse resolution, based on inverting

2156-441: The same predicate symbol and negated/unnegated status. Then, the least general generalisation is obtained as the disjunction of the least general generalisations of the individual selections, which can be obtained by first-order syntactical anti-unification . To account for background knowledge, inductive logic programming systems employ relative least general generalisations , which are defined in terms of subsumption relative to

2205-562: The search for promising clauses from that of the theory: the space of clauses is explored with a beam search , while the space of theories is searched greedily . [REDACTED]  This article incorporates text from a free content work. Licensed under CC-BY 4.0 ( license statement/permission ). Text taken from A History of Probabilistic Inductive Logic Programming​ , Fabrizio Riguzzi, Elena Bellodi and Riccardo Zese, Frontiers Media . Automatic programming In computer science , automatic programming

2254-429: The space of possible clauses forms a complete lattice under the subsumption relation, where one clause C 1 {\textstyle C_{1}} subsumes another clause C 2 {\textstyle C_{2}} if there is a substitution θ {\textstyle \theta } such that C 1 θ {\textstyle C_{1}\theta } ,

2303-448: The structure and function of proteins. Unlike the focus on automatic programming inherent in the early work, these fields used inductive logic programming techniques from a viewpoint of relational data mining . The success of those initial applications and the lack of progress in recovering larger traditional logic programs shaped the focus of the field. Recently, classical tasks from automated programming have moved back into focus, as

2352-515: The theory in order to maximize the probability of a given set of positive and negative examples. No new clause can be added to the theory. In the same year, Meert, W. et al. introduced a method for learning parameters and structure of ground probabilistic logic programs by considering the Bayesian networks equivalent to them and applying techniques for learning Bayesian networks. ProbFOIL, introduced by De Raedt and Ingo Thon in 2010, combined

2401-432: Was introduced by Stephen Muggleton in 1995. In 1996, it was used by Ashwin Srinivasan, Muggleton, Michael Sternberg and Ross King to predict the mutagenic activity in nitroaromatic compounds . This was considered a landmark application for inductive logic programming , as a general purpose inductive learner had discovered results that were both novel and meaningful to domain experts. Progol proved very influential in

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