Temporal equilibrium logic: a survey

@article{Aguado2013TemporalEL,
  title={Temporal equilibrium logic: a survey},
  author={Felicidad Aguado and Pedro Cabalar and Mart{\'i}n Di{\'e}guez and Gilberto P{\'e}rez and Concepci{\'o}n Vidal Mart{\'i}n},
  journal={Journal of Applied Non-Classical Logics},
  year={2013},
  volume={23},
  pages={2 - 24}
}
Abstract This paper contains a survey of the main definitions and results obtained to date related to Temporal Equilibrium Logic, a nonmonotonic hybrid approach that combines Equilibrium Logic (the best-known logical characterisation for the stable models semantics of logic programs) with Linear-Time Temporal Logic. 

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.

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.

Temporal Equilibrium Logic with past operators

TLDR
It is shown that Kamp’s translation can also be used to translate the new extension of TEL with past operators into Quantified Equilibrium Logic, and a method for removing past operators is provided that consists in replacing past-time subformulas by fresh auxiliary atoms.

Strong Equivalence of Non-Monotonic Temporal Theories

TLDR
It is proved that equivalence in the logic of Temporal Here-and-There (THT) is not only a sufficient, but also a necessary condition for strong equivalence of two Temporal Equilibrium Logic (TEL) theories.

A G\"odel Calculus for Linear Temporal Logic

TLDR
This paper provides a deductive calculus for GTL, and shows this calculus to be sound and complete for the above-mentioned semantics.

Stable Models for Temporal Theories - - Invited Talk -

TLDR
An overview on an hybrid formalism that combines the syntax of Linear-time Temporal Logic with a non-monotonic selection of models based on Equilibrium Logic, constituting a suitable formal framework for the specification and verification of dynamic scenarios in Answer Set Programming (ASP).

Strong Equivalence of Non-monotonic Temporal Theories ( extended version ) ∗

TLDR
It is proved that equivalence in the logic of THT is not only a sufficient, but also a necessary condition for strong equivalence of two TEL theories, which reinforces the need of THt as a suitable monotonic basis for TEL.

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.

Explicit Negation in Linear-Dynamic Equilibrium Logic

TLDR
It is proved that some temporal operators that were not inter-definable, become so if the authors allow the use of explicit negation, and a new temporal operator called “while,” that is an implicational dual of “until” and may be useful as a basic connective for temporal logic programming.

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.

References

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TLDR
An extension of Equilibrium Logic consisting in the inclusion of modal temporal operators, as those used in Linear Temporal Logic, is introduced, resulting in a very expressive formalism that allows nonmonotonic reasoning for temporal domains.

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TLDR
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TLDR
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