Integrating Temporal Extensions of Answer Set Programming

In this paper we study the relation between the two main extensions of Answer Set Programming with temporal modal operators:

Temporal Equilibrium Logic

(TEL) and

Temporal Answer Sets

(TAS). On the one hand, TEL is a complete non-monotonic logic that results from the combination of Linear-time Temporal Logic (LTL) with Equilibrium Logic. On the other hand, TAS is based on a richer modal approach, Dynamic LTL (DLTL), whereas its non-monotonic part relies on a reduct-based definition for a particular limited syntax. To integrate both approaches, we propose a Dynamic Linear-time extension of Equilibrium Logic (DTEL) that allows accommodating both TEL and TAS as particular cases. With respect to TEL, DTEL incorporates more expressiveness thanks to the addition of dynamic logic operators, whereas with respect to TAS, DTEL provides a complete non-monotonic semantics applicable to arbitrary theories. In the paper, we identify cases in which both formalisms coincide and explain how this relation can be exploited for adapting existing TEL and TAS computation methods to the general case of DTEL.