Concepción Vidal

Strongly Equivalent Temporal Logic Programs

This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical characterisation of ASP) and its monotonic basis, the intermediate logic of Here-and-There (HT). Trivially, equivalence in this temporal extension of HT provides a sufficient condition for temporal strong equivalence and, as we show in the paper, it 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. The paper shows an example of the potential utility of this method by detecting some redundant rules in a simple actions reasoning scenario.

Temporal equilibrium logic: a survey

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.

Integrating Temporal Extensions of Answer Set Programming

In this paper we study the relation between the two main extensions of Answer Set Programming with temporal modal operators: Temporal Equilibrium Logic TEL and Temporal Answer Sets TAS. On the one hand, TEL is a complete non-monotonic logic that results from the combination of Linear-time Temporal Logic LTL with Equilibrium Logic. On the other hand, TAS is based on a richer modal approach, Dynamic LTL DLTL, whereas its non-monotonic part relies on a reduct-based definition for a particular limited syntax. To integrate both approaches, we propose a Dynamic Linear-time extension of Equilibrium Logic DTEL that allows accommodating both TEL and TAS as particular cases. With respect to TEL, DTEL incorporates more expressiveness thanks to the addition of dynamic logic operators, whereas with respect to TAS, DTEL provides a complete non-monotonic semantics applicable to arbitrary theories. In the paper, we identify cases in which both formalisms coincide and explain how this relation can be exploited for adapting existing TEL and TAS computation methods to the general case of DTEL.

Paving the Way for Temporal Grounding.

In this paper we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. We provide 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.

An infinitary encoding of temporal equilibrium logic

This paper studies the relation between two recent extensions of propositional Equilibrium Logic, a well-known logical characterisation of Answer Set Programming. In particular, we show how Temporal Equilibrium Logic, which introduces modal operators as those typically handled in Linear-Time Temporal Logic (LTL), can be encoded into Infinitary Equilibrium Logic, a recent formalisation that allows the use of infinite conjunctions and disjunctions. We prove the correctness of this encoding and, as an application, we further use it to show that the semantics of the temporal logic programming formalism called TEMPLOG is subsumed by Temporal Equilibrium Logic.

Genetic Algorithms in Coq: Generalization and Formalization of the Crossover Operator

In this article we present the implementation and formal verification, using the Coq system, of a generalized version of the crossover operator applied to genetic algorithms (GA). The first part of this work defines the multiple crossover of two lists in any finite number of points, generalizing a previous definition by Uchibori. In the second part, we show that the definition does not depend on the order of the list of points. Then, a more efficient definition of the crossover operation is provided, and formally proved to be equivalent to the previous one, exploiting the notion of difference list.

Certified genetic algorithms: crossover operators for permutations

In the context of Genetic Algorithms, the use of permutations for representing the chromosomes, instead of the most common binary encoding, has turned out to be more natural and convenient in order to resolve some optimization problems. With the purpose of adapting the classical crossover to this special representation, several proposals can be found in the literature [2,3,8]. In this paper we use Coq to formally implement some of these crossover operators and also to verify that they satisfy the required specifications. As we have considered permutations of (possibly) repeated elements, we can cover a wider collection of applications.

Temporal Equilibrium Logic with past operators

Abstract In this paper, we study the introduction of modal past temporal operators in Temporal Equilibrium Logic (TEL), an hybrid formalism that mixes linear-time modalities and logic programs interpreted under stable models and their characterisation in terms of Equilibrium Logic. We show that Kamp’s translation can also be used to translate the new extension of TEL with past operators into Quantified Equilibrium Logic. Additionally, we provide a method for removing past operators that consists in replacing past-time subformulas by fresh auxiliary atoms, obtaining an equivalent formula, modulo the original alphabet.

Verification for ASP denotational semantics: a case study using the PVS theorem prover

In this paper we present an encoding of the (recently proposed) denotational semantics for Answer Set Programming (ASP) and its monotonic basis into the input language of the theorem prover PVS. Using some libraries and features from PVS, we have obtained semiautomated proofs for several fundamental properties of ASP. In this way, to the best of our knowledge, we provide the first known application of formal verification to ASP.