  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.
