Functional Answer Set Programming

TL;DR

This paper extends Answer Set Programming to handle partial functions by introducing QELF, enabling more accurate knowledge representation and practical computation of answer sets using standard ASP solvers.

Contribution

It proposes QELF, a novel extension of QEL that differentiates between partial and Herbrand functions, improving the treatment of equality in ASP.

Findings

QELF allows translation of programs with partial functions into standard ASP.

The approach connects to Scott's Logic of Existence for theoretical grounding.

Practical extension enables computation of answer sets with existing ASP solvers.

Abstract

In this paper we propose an extension of Answer Set Programming (ASP), and in particular, of its most general logical counterpart, Quantified Equilibrium Logic (QEL), to deal with partial functions. Although the treatment of equality in QEL can be established in different ways, we first analyse the choice of decidable equality with complete functions and Herbrand models, recently proposed in the literature. We argue that this choice yields some counterintuitive effects from a logic programming and knowledge representation point of view. We then propose a variant called QELF where the set of functions is partitioned into partial and Herbrand functions (we also call constructors). In the rest of the paper, we show a direct connection to Scott's Logic of Existence and present a practical application, proposing an extension of normal logic programs to deal with partial functions and equality, so that they can be translated into function-free normal programs, being possible in this way to compute their answer sets with any standard ASP solver.