Logic Programming with Default, Weak and Strict Negations

TL;DR

This paper explores a logic programming framework incorporating default, weak, and strict negations, establishing a 3-valued logic model theory and a sound procedural method for reasoning with these negations.

Contribution

It introduces a novel approach to logic programming with three types of negation, along with a sound procedural method based on 3-valued logic model theory.

Findings

Developed a 3-valued logic model theory for three negation types

Constructed a sound procedural method for negations

Ensured soundness of the procedure within the 3-valued logic framework

Abstract

This paper treats logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.