A sound and complete semantics for a similarity-based logic programming language

Similarity-based Logic Programming replaces the syntactic unification algorithm of classical SLD-resolution by a fuzzy one, leading to an operational mechanism that we name Weak SLD-resolution. This is the operational semantics of a subset of Bousi∼Prolog, an extension of Prolog aiming at making the query answering process more flexible. In this paper, after recalling the model-theoretic and fixpoint semantics for a pure subset of this language, we detail the operational semantics of Bousi∼Prolog and we prove, among other results, its soundness and completeness. Significantly, throughout this work we also clarify some of the differences between our framework and other related proposals.