Super Logic Programs

TL;DR

This paper introduces super logic programs as a natural extension of standard logic programs within Autoepistemic Logic, providing new semantic characterizations and practical algorithms for query answering.

Contribution

It offers two novel characterizations of the static semantics of super logic programs, simplifying fixed point computations and enabling finite model representations.

Findings

Simplified syntactic fixed point characterization

Finite representations of static expansions via Kripke models

A web-based query-answering interpreter for super programs

Abstract

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.