A free logic for stable models with partial intensional functions

Abstract

In this paper we provide a new logical characterisation of stable models with partial functions that consists in a free-logic extension of Quantified Equilibrium Logic (QEL). In so-called “free” logics, terms may denote objects that are outside the domain of quantification, something that can be immediately used to capture partial functions.We show that this feature can be naturally accommodated in the monotonic basis of QEL (the logic of Quantified Here-and-There, QHT) by allowing variable quantification domains that depend on the world where the formula is being interpreted. The paper provides two main contributions: (i) a correspondence with Cabalar’s semantics for stable models with partial functions; and (ii) a Gentzen system for free QHT, the monotonic basis of free QEL.