Environment

This library provides predicates for environment manipulation (consulting programs, lattices and similarity relations).

A FASILL program is a tuple $\langle\Pi, \mathcal{R}, L\rangle$ where $\Pi$ is a set of rules, $\mathcal{R}$ is a similarity relation between the elements of the signature $\Sigma$ of $\Pi$, and $L$ is a complete lattice. A rule has the form $A \leftarrow \mathcal{B}$, where $A$ is an atomic formula called head and $\mathcal{B}$, called body, is a well-formed formula (built from atomic formulas $B_1, \dots, B_n$, truth values of the lattice and connectives).

All relevant components of each lattice can be encapsulated inside a Prolog file which must contain the definitions of a minimal set of predicates defining the set of valid elements, the full or partial ordering established among them, as well as the repertoire of fuzzy connectives which can be used for their subsequent manipulation.

Given a domain $\mathcal{U}$ and a lattice $L$ with a fixed t-norm, a similarity relation $\mathcal{R}$ is a fuzzy binary relation on $\mathcal{U}$ fulfilling the reflexive, symmetric and transitive properties. FASILL takes a set of similarity equations $f/n \sim g/n = r$, where $f$ and $g$ are propositional variables or constants and $r$ is an element of $L$, and generates a valid similarity relation by applying the reflexive, symmetric and transitive closures over the initial scheme.