Temporal Answer Set Programming on Finite Traces

@article{Cabalar2018TemporalAS,
  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},
  year={2018},
  volume={18},
  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

TLDR
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

TLDR
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

TLDR
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).

Quantitative and Stream Extensions of Answer Set Programming

TLDR
This work focuses on the Logic-based framework for Analytic Reasoning over Streams (LARS) and the input language was extended with operators like ♦, corresponding to existential quantification over time points.

Automata for dynamic answer set solving: Preliminary report

TLDR
This preliminary study investigates different ways of implementing temporal constraints expressed in an extension of Answer Set Programming with language constructs from dynamic logic and proposes two transformations of dynamic formulas into monadic second-order formulas.

Temporal Modalities in Answer Set Programming

TLDR
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

TLDR
This work develops the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic on the same semantic underpinnings as its predecessors and thus uses a simple time domain of bounded time steps.

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

TLDR
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

TLDR
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

TLDR
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.

References

SHOWING 1-10 OF 25 REFERENCES

STeLP - A Tool for Temporal Answer Set Programming

TLDR
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

TLDR
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

TLDR
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
TLDR
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

TLDR
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*

TLDR
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

TLDR
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

TLDR
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)

TLDR
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