Partial Functions and Equality in Answer Set Programming

In this paper we propose an extension of Answer Set Programming (ASP) [1], and in particular, of its most general logical counterpart, Quantified Equilibrium Logic (QEL) [2], 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 [3]. 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

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

[4] 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.