@book {5494,
title = {Fuzzy Description Logics from a Mathematical Fuzzy Logic point of view},
series = {Monografies de l{\textquoteright}Institut d{\textquoteright}Investigaci{\'o} en Intel{\textperiodcentered}lig{\`e}ncia Artificial},
year = {Enviado},
pages = {220},
publisher = {IIIA - CSIC},
organization = {IIIA - CSIC},
address = {Bellaterra},
abstract = {Description Logic is a formalism that is widely used in the framework of Knowledge Representation and Reasoning in Artificial Intelligence. It is based on Classical Logic in order to guarantee the correctness of the inferences on the required reasoning tasks. It is indeed a fragment of First Order Predicate Logic whose language is strictly related to the one of Modal Logic. Fuzzy Description Logic is the generalization of the classical Description Logic framework thought for reasoning with vague concepts that often arise in practical applications. Fuzzy Description Logic has been investigated since the last decade of the 20th century. During the first fifteen years of investigation its semantics has been based on Fuzzy Set Theory. A semantics based on Fuzzy Set Theory, however, has been shown to have some counter-intuitive behavior, due to the fact that the truth function for the implication used is not the residuum of the truth function for the conjunction. In the meanwhile, Fuzzy Logic has been given a formal framework based on Many-valued Logic. This framework, called Mathematical Fuzzy Logic, has been proposed has the kernel of a mathematically well founded Fuzzy Logic. In this monography we propose a Fuzzy Description Logic whose semantics is based on Mathematical Fuzzy Logic as its mathematically well settled kernel. To this end we provide a novel notation that is strictly related to the notation that is used in Mathematical Fuzzy Logic. After having settled the notation, we investigate the hierarchies of description languages over different t-norm based semantics and the reductions that can be performed between reasoning tasks. The new framework that we establish gives us the possibility to systematically investigate the relation of Fuzzy Description Logic to Fuzzy First Order Logic and Fuzzy Modal Logic. Next we provide some (un)decidability results for the case of infinite t-norm based semantics with or without knowledge bases. Finally we investigate the complexity bounds of reasoning tasks without knowledge bases for basic Fuzzy Description Logics over finite t-norms.},
keywords = {Description Logics, Many-valued Modal Logic, mathematical fuzzy logic},
author = {Marco Cerami}
}
@inbook {5108,
title = {On possibilistic modal logics defined over MTL-chains},
booktitle = {Petr H{\'a}jek on Mathematical Fuzzy Logic},
number = {6},
year = {2015},
pages = {225-244},
publisher = {Springer},
organization = {Springer},
edition = {Franco Montagna},
abstract = {In this paper we revisit a 1994 paper by H{\'a}jek et al. where a modal logic over a finitely-valued Lukasiewicz logic is defined to capture possibilistic reasoning. In this paper we go further in two aspects: first, we generalize the approach in the sense of considering modal logics over an arbitrary finite MTL-chain, and second, we consider a different possibilistic semantics for the necessity and possibility modal operators. The main result is a completeness proof that exploits similar techniques to the ones involved in H{\'a}jek et al.{\textquoteright}s previous work.},
keywords = {Fuzzy Logic, Many-valued Modal Logic, Possibitistic Logic},
url = {http://link.springer.com/chapter/10.1007/978-3-319-06233-4_11},
author = {F{\`e}lix Bou and Francesc Esteva and Llu{\'\i}s Godo},
editor = {Franco Montagna}
}
@conference {5251,
title = {Axiomatising a fuzzy modal logic over the standard product algebra},
booktitle = {Logic, Algebra and Truth Degrees 2014 (LATD 2014)},
year = {2014},
month = {16/07/2014},
pages = {275-279},
edition = {M. Baaz, A. Ciabattoni, S. Hetzl},
address = {Vienna, Austria},
keywords = {Many-valued Modal Logic, mathematical fuzzy logic, modal logic, product logic},
url = {http://www.logic.at/latd2014/abstract_booklet_final.pdf},
author = {Amanda Vidal and Francesc Esteva and Llu{\'\i}s Godo}
}