# 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.

## 42 Citations

### An infinitary encoding of temporal equilibrium logic*

- Philosophy, Computer ScienceTheory and Practice of Logic Programming
- 2015

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

- Computer Science2015 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

- PhilosophyJ. Appl. Non Class. Logics
- 2017

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

- PhilosophyKR
- 2014

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

- Philosophy, Computer Science
- 2022

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 -

- Computer ScienceLPNMR
- 2015

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 ) ∗

- Computer Science
- 2014

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

- Computer ScienceTheory and Practice of Logic Programming
- 2020

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

- PhilosophyECAI
- 2020

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

- Computer ScienceTheory and Practice of Logic Programming
- 2021

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.

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