7,857 research outputs found

    Automatic Proving of Fuzzy Formulae with Fuzzy Logic Programming and SMT

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    In this paper we deal with propositional fuzzy formulae containing severalpropositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool. We firstly recall an SMT (Satisfiability Modulo Theories) based method for automatically proving theorems in relevant infinitely valued (including Łukasiewicz and G¨odel) logics. Next, instead of focusing on satisfiability (i.e., proving the existence of at least one model) or unsatisfiability, our interest moves to the problem of finding the whole set of models (with a finite domain) for a given fuzzy formula. We propose an alternative method based on fuzzy logic programming where the formula is conceived as a goal whose derivation tree contains on its leaves all the models of the original formula, by exhaustively interpreting each propositional symbol in all the possible forms according the whole setof values collected on the underlying lattice of truth-degrees

    A generic ATMS

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    AbstractThe main aim of this paper is to create a general truth maintenance system based on the De Kleer algorithm. This system (the ATMS) is to be designed so that it can be used in different propositional monotonic logic models of reasoning systems. The knowledge base system that will interact with it is described. Furthermore, we study the efficiency that transferring the ATMS to a logic with several truth values presupposes. Definitions and properties of the generic ATMS are particularized to interact both with a reasoning system based on multivalued logic specifically for the case of [0, 1 ]-valued logic and with a reasoning system based on fuzzy logic. The latter will be designed to reason with fuzzy truth values, although a parallel project might be followed using linguistic labels directly

    Compactness of first-order fuzzy logics

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    One of the nice properties of the first-order logic is the compactness of satisfiability. It state that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in many-valued logics, poses various kind of the compactness in these logics. One of this issues is the compactness of KK-satisfiability. Here, after an overview on the results around the compactness of satisfiability and compactness of KK-satisfiability in many-valued logic based on continuous t-norms (basic logic), we extend the results around this topic. To this end, we consider a reverse semantical meaning for basic logic. Then we introduce a topology on [0,1][0,1] and [0,1]2[0,1]^2 that the interpretation of all logical connectives are continuous with respect to these topologies. Finally using this fact we extend the results around the compactness of satisfiability in basic ogic
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