On the Relation between Weak Completion Semantics and Answer Set Semantics

TL;DR

This paper explores the relationship between Weak Completion Semantics and Answer Set Semantics, providing translations and comparisons to understand their differences and similarities in logic programming.

Contribution

It introduces a translation method from WCS to ASP, clarifying their correspondence and differences through formal representations and examples.

Findings

WCS and ASP have different underlying three-valued logics.

Logic programs under WCS can be translated into ASP using definition completion.

The translation helps in understanding the formal relationship between the two semantics.

Abstract

The Weak Completion Semantics (WCS) is a computational cognitive theory that has shown to be successful in modeling episodes of human reasoning. As the WCS is a recently developed logic programming approach, this paper investigates the correspondence of the WCS with respect to the well-established Answer Set Semantics (ASP). The underlying three-valued logic of both semantics is different and their models are evaluated with respect to different program transformations. We first illustrate these differences by the formal representation of some examples of a well-known psychological experiment, the suppression task. After that, we will provide a translation from logic programs understood under the WCS into logic programs understood under the ASP. In particular, we will show that logic programs under the WCS can be represented as logic programs under the ASP by means of a definition completion, where all defined atoms in a program must be false when their definitions are false.