Computing and Comparing Semantics of Programs in Multi-valued Logics

TL;DR

This paper introduces parameterized semantics for logic programs within multi-valued bilattice logics, unifying and extending existing semantics like well-founded and Kripke-Kleene by allowing assumptions for undefined atoms.

Contribution

It proposes a unified framework for semantics of logic programs using parameterization in multi-valued bilattice logics, extending Fitting's semantics and enabling comparison and combination of different assumptions.

Findings

Defines a simple operator for computing parameterized semantics.

Shows the framework captures and extends conventional logic program semantics.

Unifies various semantics within a single parameterized approach.

Abstract

The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propose to unify and extend this assumption-based approach by introducing parameterized semantics for logic programs. The parameter holds the value that one assumes for all atoms whose logical values cannot be inferred from the rules. We work within multi-valued logic with bilattice structure, and we consider the class of logic programs defined by Fitting. Following Fitting's approach, we define a simple operator that allows us to compute the parameterized semantics, and to compare and combine semantics obtained for different values of the parameter. The semantics proposed by Fitting corresponds to the value false. We also show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation.