Vicious Circle Principle and Logic Programs with Aggregates

TL;DR

This paper introduces $log$, a logic programming language extending ASP with aggregates, emphasizing simplicity, clear semantics, and providing an answer set computation algorithm and comparative analysis.

Contribution

It presents a new knowledge representation language with aggregates, offering a simple syntax, well-defined semantics, and an answer set computation method.

Findings

$log$ has desirable properties and clear semantics.

An algorithm for computing answer sets is provided.

Comparison with other approaches demonstrates its effectiveness.

Abstract

The paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.