Circumscription and Projection as Primitives of Logic Programming

We pursue a representation of logic programs as classical first-order sentences. Different semantics for logic programs can then be expressed by the way in which they are wrapped into – semantically defined – operators for circumscription and projection. (Projection is a generalization of second-order quantification.) We demonstrate this for the stable model semantics, Clark’s completion and a three-valued semantics based on the Fitting operator. To represent the latter, we utilize the polarity sensitiveness of projection, in contrast to second-order quantification, and a variant of circumscription that allows to express predicate minimization in parallel with maximization. In accord with the aim of an integrated view on different logic-based representation techniques, the material is worked out on the basis of first-order logic with a Herbrand semantics. Table of Contents

• Type: Conference
• Year: 2010
• Where: ICLP
• Authors: Christoph Wernhard
• Keywords: Automated Reasoning, Classical first-order Sentences, ICLP 2010, Logic Programs, Second-order Quantification