José Gaintzarain Ibarmia

• PhD in Computer Science
• Professor at University of the Basque Country

We provide an extended abstract of the article with the same title and authors published in the journal ACM Transactions on Computational Logic, Vol. 14, No. 4, Article 28, November 2013, DOI: http://dx.doi.org/10.1145/2528931.

In this paper, we present a declarative propositional temporal logic programming language called TeDiLog that is a combination of the temporal and disjunctive paradigms in Logic Programming. TeDiLog is, syntactically, a sublanguage of the well-known Propositional Linear-time Temporal Logic (PLTL). TeDiLog allows both eventualities and always-formul...

(Extended abstract of the article published with the same title and by the same authors in Journal of Automated Reasoning 50(1): 1-49, 2013; DOI 10.1007/s10817-011-9241-2) (See also http://www.slideshare.net/sistedes2012/invariantfree-clausal-temporal-resolution)

In this thesis we propose a new approach to deduction methods for temporal logic. Our proposal is based on an inductive definition of eventualities that is different from the usual one. On the basis of this non-customary inductive definition for eventualities, we first provide dual systems of tableaux and sequents for Propositional Linear-time Temp...

Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires to generate invariants for performing resolution on eventua...

In this paper we report on a prototype that implements a one-pass tableau method for Propositional Linear Temporal Logic (shortly, PLTL). It is well known that PLTL is decidable and that PLTL worst-case is PSPACE. The first tableau method for PLTL is due to P. Wolper in 1983 and it is a twopass method. In the first pass, it generates an auxiliary gra...

Horn ⊃ is a logic programming language which extends usual Horn clauses by adding intuitionistic implication in goals and clause bodies. This extension can be seen as a way of structuring programs in logic programming. We are interested in finding correct and efficient translations from Horn ⊃ programs into some representation type that, preserving...

On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph that must be checked and (possibly) pruned in a second phase of the refutation procedure. On the other hand, traditional sequent calculi for TL make use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their...

In this paper, we propose a new approach to define temporal logic programming languages based on a temporal extension of resolution. We introduce the very expressive language TeDiLog that allows both eventualities and always formulas to occur in the head and also in the body of clauses. The operational semantics of TeDiLog is formulated on the basi...

The better known methods of semantic tableaux for deciding satisfiability in propositional linear temporal logic generate graphs in addition to classical trees. The test of satisfaction is made from the graph and it does not correspond with the application of rules in any calculus for PLTL. We present here a new method of semantic tableaux without...

Sequent calculi usually provide a general deductive setting that uniformly embeds other proof-theoretical approaches, such as tableaux methods, resolution techniques, goal-directed proofs, etc. Unfortunately, in temporal logic, existing sequent calculi make use of a kind of inference rules that prevent the effective mechanization of temporal deduct...

Propositional Horn ⊃ clauses are a class of boolean formulas extending the propositional Horn clauses by adding intuitionistic implication in goals and clause bodies. Our aim is to study the learnability of this class. In this paper we show some given steps which yield to set the problem of learning Horn ⊃ clauses between learning boolean formulas...

Horn ⊃ is a logic programming language which extends usual Horn clauses by adding intuitionistic implication in goals and clause bodies. This extension can be seen as a form of structuring programs in logic programming. Restricted to the propositional setting of this language, we prove that any goal in Horn ⊃ can be translated into a monotone Boole...

Horn ⊃ is a logic programming language which extends usual Horn clauses with intuitionistic implication. In this paper we study the learnability of the concepts that are represented by conjunctions of propositional Horn ⊃ clauses.

We define a classical style, one-pass tableau for the full branching-time logic CTL . This work extends previously defined tableau technique for propositional linear-time temporal logic, PLTL, giving a new decision procedure for CTL . One of the core features of this method is that unlike any other known deduction for the full branching-time logic,...