Similarity-Based Strict Equality in a Fully Integrated Fuzzy Logic Language

The extension of a given similarity relation

$$\mathcal R$$

between pairs of symbols of a particular alphabet to terms built with such symbols can be implemented at a very high abstract level by a set of fuzzy program rules defining a predicate called

sse

. This predicate is defined for incorporating “Similarity-based Strict Equality” into the new fuzzy logic language

FASILL

(acronym of “Fuzzy Aggregators and Similarity Into a Logic Language”) that we have recently developed in our research group.

FASILL

aims to cope with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. In this paper we show the benefits of using this sophisticated notion of equality which is somehow inspired by the so-called “Strict Equality” of functional and functional-logic languages with lazy semantics (e.g.:

Haskell

and

Curry

respectively) and the “Similarity-based Equality” of fuzzy logic languages using weak unification (

Bousi

$$\sim $$

Prolog

,

Likelog

), a notion beyond classic syntactic unification.