Temporal Answer Set Programming on Finite Traces

Abstract

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)

First-order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications

“…temporal databases [78], and answer-set programming [31][32][33]. The problem of establishing connections between finite and infinite traces semantics is also not new to the literature.…”

Reactive Answer Set Programming

“…A different formalism using equilibrium temporal logic to model reactive rules is described in Cabalar et al . (2018).…”

DatalogMTL with Negation Under Stable Models Semantics

“…An important limitation of DatalogMTL in practice is that negation is disallowed in rules-indeed, motivated by a range of applications, there has recently been growing interest in logics that combine non-monotonic negation with temporal constructs (Cabalar and Vega 2007;Aguado et al 2013;Cabalar et al 2018;Beck, Dao-Tran, and Eiter 2018;Zaniolo 2012). In the context of DatalogMTL, Tena Cucala et al (2021) recently proposed an extension of the language with stratified negation as failure and showed that the additional expressive power does not increase complexity of reasoning regardless of whether we consider the rational or the integer timeline (Wałęga et al 2020).…”

“…Our setting is closely related to recent research on combining answer set programming (ASP) with temporal logics. For example, the logic TEL (Cabalar and Vega 2007;Aguado et al 2013;Cabalar et al 2018) combines ASP with linear temporal logic, and the LARS language combines ASP with window-based temporal constructs for stream reasoning (Beck, Dao-Tran, and Eiter 2018). The logic recently proposed by Cabalar et al (2020) is maybe the closest to our work, as it combines stable models semantics with propositional MTL interpreted over the natural numbers; this logic, however, is rather different from DatalogMTL, where the use of logical connectives and MTL operators is restricted in the spirit of Datalog to disallow disjunction and "existential" MTL operators (such as diamond, since, or until operators) in rule heads.…”