Temporal equilibrium logic: a survey

  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},
  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*

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
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

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

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

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 -

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 ) ∗

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

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

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

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.



Temporal Equilibrium Logic: A First Approach

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.

Equilibrium logic

  • D. Pearce
  • Economics
    Annals of Mathematics and Artificial Intelligence
  • 2006
This work presents an overview of equilibrium logic and its main properties and uses and states it provides a logical foundation for ASP as an extension of the basic syntax of answer set programs.

Propositional theories are strongly equivalent to logic programs

Any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly with negation in the head, under the answer sets semantics.

A New Logical Characterisation of Stable Models and Answer Sets

This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics with equilibrium logic, and shows that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz.

The Logic of Persistence

A way of representing persistence in a framework based on a generalization of circumscription, which captures Hanks and McDermott's procedural representation is presented.

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.

A Resolution Method for Temporal Logic

The resolution method is based on classical resolution, but incorporates a temporal resolution rule that can be implemented efficiently using a graph-theoretic approach.

A New Perspective on Stable Models

A new definition of a stable model is proposed, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and is based on a syntactic transformation, which turns a logic program into a formula of second-order logic that is similar to the formula familiar from the definition of circumscription.

Strongly Equivalent Temporal Logic Programs

A linear temporal extension of Equilibrium Logic and its monotonic basis, the intermediate logic of Here-and-There (HT), provides a sufficient condition for temporal strong equivalence and can be transformed into a provability test into the standard Linear Temporal Logic (LTL), something that can be automatically checked using any of the LTL available provers.

Paving the Way for Temporal Grounding

This paper provides several fundamental contributions that pave the way for the implementation of a grounding process, that is, a method that allows replacing variables by ground instances in all the possible (or better, relevant) ways.