Temporal Answer Set Programming on Finite Traces

  title={Temporal Answer Set Programming on Finite Traces},
  author={Pedro Cabalar and Roland Kaminski and Torsten Schaub and Anna Schuhmann},
  journal={Theory and Practice of Logic Programming},
  pages={406 - 420}
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… 

Linear-Time Temporal Answer Set Programming

This survey presents an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving and obtains a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL.

Implementing Dynamic Answer Set Programming

The reduction of dynamic formulas to temporal logic programs allows to extend ASP with both approaches in a uniform way and to implement both extensions via temporal ASP solvers such as telingo.

Dynamic and Temporal Answer Set Programming on Linear Finite Traces

An expressive non-monotonic modal logic, which extends traditional temporal logic programming approaches to the general syntax of LTL and possesses a computational complexity beyond LTL (Bozzelli and Pearce, 2015).

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Automata for dynamic answer set solving: Preliminary report

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Temporal Modalities in Answer Set Programming

A temporal extension of ASP called Temporal Equilibrium Logic (TEL) was proposed in and extensively studied later and is an expressive non-monotonic modal logic that shares the syntax of Linear-Time Temporal Logic but interprets temporal formulas under a non-Monotonic semantics that properly extends stable models.

Towards Metric Temporal Answer Set Programming

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

This paper investigates preservation of equivalences and satisfiability of formulas between finite and infinite traces, and provides a set of semantic and syntactic conditions to guarantee when the distinction between reasoning in the two cases can be blurred.

telingo = ASP + Time

Telingo is described, an extension of the ASP system clingo with temporal operators over finite linear time and insights into its implementation are provided and an empirical evaluation contrasting standard incremental ASP programs with their temporal counterparts in telingo’s input language is provided.

Temporal Logic Programs with Temporal Description Logic Axioms

A combination of Answer Set Programming (ASP) and Description Logics (DL) on top of a modal temporal basis using connectives from Linear-time Temporal Logic (LTL), which actually interprets \(\mathcal{ALC}\) axioms in terms of their translation into first order sentences, so that the semantics of TEL is eventually used in the background.



STeLP - A Tool for Temporal Answer Set Programming

STeLP, a solver for Answer Set Programming with temporal operators, obtains its set of temporal equilibrium models (a generalisation of stable models for this extended syntax) in terms of a deterministic Buchi automaton capturing the complete program behaviour.

Automata-Based Computation of Temporal Equilibrium Models

This paper proposes a method for the latter that consists in building a Buchi automaton that accepts exactly the temporal equilibrium models of a given theory, providing an automata-based decision procedure and illustrating the ω-regularity of such sets.

A Normal Form for Linear Temporal Equilibrium Logic

This paper shows that TEL can be similarly reduced to a normal form consisting of a set of implications quite close to logic program rules, useful both for a practical implementation of TEL and a simpler analysis of theoretical problems.

On the Complexity of Temporal Equilibrium Logic

  • L. BozzelliD. Pearce
  • Computer Science
    2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
  • 2015
This paper provides a systematic complexity analysis for the (consistency) problem of checking the existence of a temporal equilibrium model of a TEL formula, establishing a lower bound matching the EXPSPACE upper bound.

Linear Temporal Logic and Linear Dynamic Logic on Finite Traces

This paper shows that LTLf, i.e., LTL under this assumption, is less expressive than what might appear at first sight, and proposes a logic, LDLf for Linear Dynamic Logic over finite traces, which borrows the syntax from Propositional Dynamic Logic (PDL), but is interpreted over finite trace.

An infinitary encoding of temporal equilibrium logic*

It is shown how Temporal Equilibrium Logic, which introduces modal operators as those typically handled in Linear-Time Temporal Logic, can be encoded into Infinitary Equ equilibrium Logic, a recent formalisation that allows the use of infinite conjunctions and disjunctions.

Action Language BC+: Preliminary Report

This work proposes a new action language called BC+, which closes the gap between action languages and the modern Answer Set Programming (ASP) language, and implements the language by extending system Cplus2ASP.

Multi-shot ASP solving with clingo

Clingo offers a new application programming interface that is conveniently accessible via scripting languages and abolishes the need for dedicated systems for incremental and reactive reasoning, and its flexibility goes well beyond the advanced yet still rigid solving processes of the latter.

Answer Set Planning (Abstract)

In “answer set programming”[5,7] solutions to a problem are represented by answer sets, and not by answer substitutions produced in response to a query, as in conventional logic programming.

Temporal and Modal Logic

  • E. Emerson
  • Philosophy
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990