Explicit Negation in Linear-Dynamic Equilibrium Logic

Abstract

[Abstract]: In this paper, we revisit a temporal extension of Equilibrium Logic (the logical characterisation of Answer Set Programming) that introduces Linear Dynamic Logic modalities. In particular, we further incorporate to this extension (we call Linear Dynamic Equilibrium Logic) an explicit negation operator, treated as a regular logical connective. We explain several formal properties of this new extension. For instance, we prove that some temporal operators that were not inter-definable, become so if we allow the use of explicit negation. Finally, we also introduce and study a new temporal operator called “while,” that is an implicational dual of “until” and may be useful as a basic connective for temporal logic programming.