Similarity-based Unification

Abstract

Unification plays a central rule in Logic Programming. We ”soften” the unification process by admitting that two first order expressions can be ”similar” up to a certain degree and not necessarly identical. An extension of the classical unification theory is proposed accordingly. Indeed, in our approach, inspirated by the unification algorithm of Martelli-Montanari, the systems of equations go through a series of ”sound” transformations until a solvable form is found yielding a substitution that is proved to be a most general extended unifier for the given system of equations.

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

“…In particular, given a residuated logic program without loops such that its rules can contain only one negated propositional symbol in their bodies, we will show how bipolar max-product fuzzy relation equations can be used for abductive reasoning, that is, for computing the truth values of the hypotheses from the observed values. Notice that, this framework is different from inductive reasoning, which has been widely studied in [12,24,25,28].…”

A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees

“…Fuzzy logic languages can be classified (among other criteria) regarding the emphasis they assign when fuzzifying the original unification/resolution mechanisms of PROLOG. So, whereas some approaches are able to cope with similarity/proximity relations at unification time [9,1,29], other ones extend their operational principles (maintaining syntactic unification) for managing a wide variety of fuzzy connectives and truth degrees on rules/goals beyond the simpler case of true or false [16,19,24].…”

“…Firstly, the pioneering papers [4,8,9] and [3], where the concept of unification by similarity was first developed. Note that, we share their objectives, using similarity relations as a basis, but contrary to our proposal, they use the sophisticated (but cumbersome) notions of clouds, systems of clouds and closure operators in the definition of the unification algorithm, that may endanger the efficiency of the derived operational semantics.…”

“…From a practical point of view, similarity-based approaches have produced three main experimental realizations. The first two system prototypes described in the literature were: the fuzzy logic language LIKELOG (LIKEness in LOGic) [2] (an interpreter implemented in PROLOG using rather direct techniques and the aforementioned cloud and closure concepts described in [3,4,9,8]) and SiLog [17] (an interpreter written in Java based on the ideas introduced in [29]). Neither LIKELOG nor SiLog are publicly available, what prevent a real evaluation of these systems, and they seem immature prototypes.…”

Towards an automated deduction system for first-order possibilistic logic programming with fuzzy constants

“…More recently, Gerla and Sessa 20 formalized a methodology for transforming an interpreter for SLD resolution into an interpreter that computes on abstract values that express similarity properties on the set of predicate and function symbols of a classic first-order language. Formato et al 19 extended the unification algorithm of Martelli-Montanari to allow a partial matching between crisp constants through similarity relations. In the framework of possibilistic logic, Godo and Vila 21 proposed a propositional temporal logic, with a Horn rule-style syntax and a possibilistic semantics, allowing a partial matching between fuzzy temporal constraints.…”