# Relating Two Dialects of Answer Set Programming

## TL;DR

This paper proves the equivalence of two answer set programming dialects based on different stable model semantics and explores relaxing restrictions on recursion through aggregates.

## Contribution

It demonstrates the conditions under which the two ASP dialects are equivalent and how to relax restrictions without losing this equivalence.

## Key findings

- Proves equivalence of two ASP dialects under certain conditions
- Shows how to relax restrictions on recursion through aggregates
- Provides theoretical foundations for ASP language interoperability

## Abstract

The input language of the answer set solver clingo is based on the definition of a stable model proposed by Paolo Ferraris. The semantics of the ASP-Core language, developed by the ASP Standardization Working Group, uses the approach to stable models due to Wolfgang Faber, Nicola Leone, and Gerald Pfeifer. The two languages are based on different versions of the stable model semantics, and the ASP-Core document requires, "for the sake of an uncontroversial semantics," that programs avoid the use of recursion through aggregates. In this paper we prove that the absence of recursion through aggregates does indeed guarantee the equivalence between the two versions of the stable model semantics, and show how that requirement can be relaxed without violating the equivalence property. The paper is under consideration for publication in Theory and Practice of Logic Programming.