Proximity-Based Unification: An Efficient Implementation Method

Unification is a central concept in logic systems based on the resolution principle. As well, in knowledge representation, proximity relations (i.e., reflexive, symmetric, fuzzy binary relations) are useful for introducing semantics into a syntactic level by modeling the semantic closeness of differ...

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Vydáno v:IEEE transactions on fuzzy systems Ročník 29; číslo 5; s. 1238 - 1251
Hlavní autoři: Julian-Iranzo, Pascual, Saenz-Perez, Fernando
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Approximation algorithms
Bousi<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> sim</tex-math> </inline-formula>Prolog
Cognition
Fuzzy logic
fuzzy logic programming (FLP)
fuzzy prolog
Knowledge representation
Logic programming
Prolog
Proximity
proximity relations
Semantics
Superluminescent diodes
Syntactics
weak SLD resolution
weak unification
ISSN:1063-6706, 1941-0034
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Abstract Unification is a central concept in logic systems based on the resolution principle. As well, in knowledge representation, proximity relations (i.e., reflexive, symmetric, fuzzy binary relations) are useful for introducing semantics into a syntactic level by modeling the semantic closeness of different syntactic objects and managing vague or imprecise information. Proximity relations, in combination with the unification algorithm, make possible expressing certain forms of approximate reasoning in a logic programming framework. In this article, we use proximity relations in the context of a (fuzzy) logic programming system, called Bousi <inline-formula><tex-math notation="LaTeX">\sim</tex-math></inline-formula> Prolog , as a way of solving the limitations introduced by similarity relations (i.e., transitive proximity relations) to correctly represent fuzzy information. Recently, we introduced an accurate definition of proximity between expressions (terms or atomic formulas) and a new unification algorithm able to manage proximity relations properly. However, the so-called weak unification algorithm, which is an extension of Martelli and Montanari's unification algorithm supported by the new notion of proximity, does not have an efficient implementation. In this article, we present a method that facilitates such an efficient implementation, including an adaptation of the weak SLD resolution rule based on the new unification algorithm, and its integration and implementation into the fuzzy logic programming system Bousi <inline-formula><tex-math notation="LaTeX">\sim</tex-math></inline-formula> Prolog . A performance analysis to show its efficiency is also presented.
AbstractList Unification is a central concept in logic systems based on the resolution principle. As well, in knowledge representation, proximity relations (i.e., reflexive, symmetric, fuzzy binary relations) are useful for introducing semantics into a syntactic level by modeling the semantic closeness of different syntactic objects and managing vague or imprecise information. Proximity relations, in combination with the unification algorithm, make possible expressing certain forms of approximate reasoning in a logic programming framework. In this article, we use proximity relations in the context of a (fuzzy) logic programming system, called Bousi <inline-formula><tex-math notation="LaTeX">\sim</tex-math></inline-formula> Prolog , as a way of solving the limitations introduced by similarity relations (i.e., transitive proximity relations) to correctly represent fuzzy information. Recently, we introduced an accurate definition of proximity between expressions (terms or atomic formulas) and a new unification algorithm able to manage proximity relations properly. However, the so-called weak unification algorithm, which is an extension of Martelli and Montanari's unification algorithm supported by the new notion of proximity, does not have an efficient implementation. In this article, we present a method that facilitates such an efficient implementation, including an adaptation of the weak SLD resolution rule based on the new unification algorithm, and its integration and implementation into the fuzzy logic programming system Bousi <inline-formula><tex-math notation="LaTeX">\sim</tex-math></inline-formula> Prolog . A performance analysis to show its efficiency is also presented.
Unification is a central concept in logic systems based on the resolution principle. As well, in knowledge representation, proximity relations (i.e., reflexive, symmetric, fuzzy binary relations) are useful for introducing semantics into a syntactic level by modeling the semantic closeness of different syntactic objects and managing vague or imprecise information. Proximity relations, in combination with the unification algorithm, make possible expressing certain forms of approximate reasoning in a logic programming framework. In this article, we use proximity relations in the context of a (fuzzy) logic programming system, called Bousi [Formula Omitted] Prolog , as a way of solving the limitations introduced by similarity relations (i.e., transitive proximity relations) to correctly represent fuzzy information. Recently, we introduced an accurate definition of proximity between expressions (terms or atomic formulas) and a new unification algorithm able to manage proximity relations properly. However, the so-called weak unification algorithm, which is an extension of Martelli and Montanari's unification algorithm supported by the new notion of proximity, does not have an efficient implementation. In this article, we present a method that facilitates such an efficient implementation, including an adaptation of the weak SLD resolution rule based on the new unification algorithm, and its integration and implementation into the fuzzy logic programming system Bousi [Formula Omitted] Prolog . A performance analysis to show its efficiency is also presented.
Author Julian-Iranzo, Pascual
Saenz-Perez, Fernando
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Approximation algorithms
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Cognition
Fuzzy logic
fuzzy logic programming (FLP)
fuzzy prolog
Knowledge representation
Logic programming
Prolog
Proximity
proximity relations
Semantics
Superluminescent diodes
Syntactics
weak SLD resolution
weak unification
Title Proximity-Based Unification: An Efficient Implementation Method
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