Grounding Bound Founded Answer Set Programs

TL;DR

This paper introduces flattening and grounding techniques for Bound Founded Answer Set Programming (BFASP), enabling more efficient program solving by reducing ground program size through extended ASP methods.

Contribution

It extends ASP grounding and magic set transformations to BFASP, facilitating efficient handling of complex non-ground expressions in BFASP programs.

Findings

Flattening arbitrary BFASP expressions to primitive forms.

Extended grounding techniques significantly reduce program size.

Improved solving efficiency demonstrated in implementation.

Abstract

To appear in Theory and Practice of Logic Programming (TPLP) Bound Founded Answer Set Programming (BFASP) is an extension of Answer Set Programming (ASP) that extends stable model semantics to numeric variables. While the theory of BFASP is defined on ground rules, in practice BFASP programs are written as complex non-ground expressions. Flattening of BFASP is a technique used to simplify arbitrary expressions of the language to a small and well defined set of primitive expressions. In this paper, we first show how we can flatten arbitrary BFASP rule expressions, to give equivalent BFASP programs. Next, we extend the bottom-up grounding technique and magic set transformation used by ASP to BFASP programs. Our implementation shows that for BFASP problems, these techniques can significantly reduce the ground program size, and improve subsequent solving.