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In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot ASP systems and benefits from an extension of ASP's full-fledged input language with temporal operators. This includes future as well as past operators whose combination offers a rich temporal modeling language. For computation, we identify the class of temporal logic programs and prove that it constitutes a normal form for our approach. Finally, we outline two implementations, a generic one and an extension of the ASP system clingo.
Under consideration for publication in Theory and Practice of Logic Programming (TPLP)
We propose a new temporal extension of the logic of Here-and-There (HT) and its equilibria obtained by combining it with dynamic logic over (linear) traces. Unlike previous temporal extensions of HT based on linear temporal logic, the dynamic logic features allow us to reason about the composition of actions. For instance, this can be used to exercise fine grained control when planning in robotics, as exemplified by GOLOG. In this paper, we lay the foundations of our approach, and refer to it as Linear Dynamic Equilibrium Logic, or simply DEL. We start by developing the formal framework of DEL and provide relevant characteristic results. Among them, we elaborate upon the relationships to traditional linear dynamic logic and previous temporal extensions of HT.