Marco Cerami

Universidade Federal da Bahia · Departamento de Matemática

The aim of the present paper is to prove that concept validity and positive satisfiability with an empty ontology in the Fuzzy Description Logic IALE, under standard product semantics and with respect to quasi-witnessed models, are decidable. In our framework we are not considering reasoning tasks over ontologies. The proof of our result consists i...

In this paper we study the relationships between a family of ALC-like fuzzy description logics (FDLs) defined over left-continuous t-norms and some many-valued multi-modal logics (MMLs). We analyze these relationships in both directions, that is, how to merge FDLs into MMLs and vice-versa. The analysis starts from the relationships between the lang...

Fuzzy Description Logics (DLs) are are a family of knowledge representation formalisms designed to represent and reason about vague and imprecise knowledge that is inherent to many application domains. Previous work has shown that the complexity of reasoning in a fuzzy DL using finitely many truth degrees is usually not higher than that of the unde...

Fuzzy Description Logics (DLs) are used to represent and reason about vague and imprecise knowledge that is inherent to many application domains. It was recently shown that the complexity of reasoning in finitely valued fuzzy DLs is often not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of th...

In this paper we explain the design and preliminary implementation of a solver for the positive satisfiability problem of concepts in a fuzzy description logic over the infinite-valued product logic. This very solver also answers 1-satisfiability in quasi-witnessed models. The solver works by firs t performing a direct reduction of the problem to a...

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALCALC with GCIs does not have the finite model property under Łukasiewicz Logic or Product Logic, the proposed reasoning algorithms are neither correct nor complete an...

Following the guidelines proposed by Hájek in [1], some proposals of research on Fuzzy Description Logics (FDLs) were given in [2]. One of them consists in the definition and development of a family of description languages, each one having as underlying fuzzy logic the expansion with an involutive negation and truth constants of the logic defined...

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable proble...

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpo...

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...

Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for dealing with vague concepts, commonly present in real applications. Following th...

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 prob...