Francesc Esteva

IJCAI Conference 2011 Conference Paper

Finite-Valued Lukasiewicz Modal Logic Is PSPACE-Complete

• F
• eacute; lix Bou
• Marco Cerami
• Francesc Esteva

It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either the Delta operator or truth constants in the language, i. e. in all these cases it is PSPACE-complete.

KR Conference 2010 Conference Paper

Decidability of a Description Logic over infinite-valued Product Logic

• Cerami Marco
• Francesc Esteva
• Felix Bou

1998), which shows the connection of fuzzy logic systems This paper proves that validity and satisfiability of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic with universal and existential quantifiers (which are non-interdefinable) is decidable when we only consider quasi-witnessed interpretations. We prove that this restriction is neither necessary for the validity problem (i. e., the validity of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic is decidable) nor for the positive satisfiability problem, because quasi-witnessed interpretations are particularly adequate for the infinite-valued Product Logic. We give an algorithm that reduces the problem of validity (and satisfiability) of assertions in our Fuzzy Description Logic (restricted to quasi-witnessed interpretations) to a semantic consequence problem, with finite number of hypothesis, on infinite-valued propositional Product Logic.

UAI Conference 1995 Conference Paper

Fuzzy logic and probability

• Petr Hájek 0001
• Lluís Godo
• Francesc Esteva

In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the differences between fuzzy logic and probability theory, here we propose a {em fuzzy} logic of probability for which completeness results (in a probabilistic sense) are provided. The main idea behind this approach is that probability values of crisp propositions can be understood as truth-values of some suitable fuzzy propositions associated to the crisp ones. Moreover, suggestions and examples of how to extend the formalism to cope with conditional probabilities and with other uncertainty formalisms are also provided.

UAI Conference 1994 Conference Paper

On Modal Logics for Qualitative Possibility in a Fuzzy Setting

• Petr Hájek 0001
• Dagmar Harmancová
• Francesc Esteva
• Pere Garcia
• Lluís Godo

Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative modal logic to the many--valued analogues MVS5 and MVKD45 of the well known modal logics of knowledge and belief S5 and KD45 respectively. Completeness results are obtained for such logics and therefore, they extend previous existing results for qualitative possibilistic logics in the classical non-fuzzy setting.

UAI Conference 1991 Conference Paper

Combining Multiple-valued Logics in Modular Expert Systems

• Jaume Agustí-Cullell
• Francesc Esteva
• Pere Garcia
• Lluís Godo
• Carles Sierra