Vicious Circle Principle and Formation of Sets in ASP Based Languages

TL;DR

This paper advances logic programming languages by extending the Alog language with infinite sets and new constructs, formalizing the Vicious Circle Principle, and introducing Slog+ with semantics aligning with existing languages for certain programs.

Contribution

It introduces Slog+, a new language formalizing the Vicious Circle Principle with more flexible set constructions and semantics compatible with established languages in specific cases.

Findings

Slog+ semantics match existing languages for non-disjunctive, finite set programs.

Extended Alog language supports infinite sets and new set constructs.

Formalization of VCP in Slog+ enhances understanding of set formation constraints.

Abstract

The paper continues the investigation of Poincare and Russel's Vicious Circle Principle (VCP) in the context of the design of logic programming languages with sets. We expand previously introduced language Alog with aggregates by allowing infinite sets and several additional set related constructs useful for knowledge representation and teaching. In addition, we propose an alternative formalization of the original VCP and incorporate it into the semantics of new language, Slog+, which allows more liberal construction of sets and their use in programming rules. We show that, for programs without disjunction and infinite sets, the formal semantics of aggregates in Slog+ coincides with that of several other known languages. Their intuitive and formal semantics, however, are based on quite different ideas and seem to be more involved than that of Slog+.