The Experts below are selected from a list of 138 Experts worldwide ranked by ideXlab platform

Carlo Nicolai - One of the best experts on this subject based on the ideXlab platform.

  • On the Costs of Nonclassical Logic
    Journal of Philosophical Logic, 2018
    Co-Authors: Volker Halbach, Carlo Nicolai
    Abstract:

    Solutions to semantic paradoxes often involve restrictions of classical Logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: (a variant) of the system KF of Feferman ( The Journal of Symbolic Logic, 56 , 1–49, 1991 ) formulated in classical Logic, and (a variant of) the system PKF of Halbach and Horsten ( The Journal of Symbolic Logic, 71 , 677–712, 2006 ), formulated in basic De Morgan Logic. The classical system is known to be much stronger than the Nonclassical one. We assess the reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.

Zhenming Song - One of the best experts on this subject based on the ideXlab platform.

  • A resolution-like strategy based on a lattice-valued Logic
    IEEE Transactions on Fuzzy Systems, 2003
    Co-Authors: Da Ruan, Yang Xu, Zhenming Song
    Abstract:

    As the use of Nonclassical Logics becomes increasingly important in computer science, artificial intelligence and Logic programming, the development of efficient automated theorem proving based on Nonclassical Logic is currently an active area of research. This paper aims at the resolution principle for the Pavelka type fuzzy Logic (1979). Pavelka showed that the only natural way of formalizing fuzzy Logic for truth-values in the unit interval [0, 1] is by using the Lukasiewicz's implication operator a/spl rarr/b=min{1,1-a+b} or some isomorphic forms of it. Hence, we first focus on the resolution principle for the Lukasiewicz Logic L/sub /spl aleph// with [0, 1] as the truth-valued set. Some limitations of classical resolution and resolution procedures for fuzzy Logic with Kleene implication are analyzed. Then some preliminary ideals about combining resolution procedure with the implication connectives in L/sub /spl aleph// are given. Moreover, a resolution-like principle in L/sub /spl aleph// is proposed and the soundness theorem of this resolution procedure is also proved. Second, we use this resolution-like principle to Horn clauses with truth-values in an enriched residuated lattice and consider the L-type fuzzy Prolog.

Volker Halbach - One of the best experts on this subject based on the ideXlab platform.

  • On the Costs of Nonclassical Logic
    Journal of Philosophical Logic, 2018
    Co-Authors: Volker Halbach, Carlo Nicolai
    Abstract:

    Solutions to semantic paradoxes often involve restrictions of classical Logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: (a variant) of the system KF of Feferman ( The Journal of Symbolic Logic, 56 , 1–49, 1991 ) formulated in classical Logic, and (a variant of) the system PKF of Halbach and Horsten ( The Journal of Symbolic Logic, 71 , 677–712, 2006 ), formulated in basic De Morgan Logic. The classical system is known to be much stronger than the Nonclassical one. We assess the reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.

Martin Peim - One of the best experts on this subject based on the ideXlab platform.

  • Clausal temporal resolution
    ACM Transactions on Computational Logic, 2001
    Co-Authors: Michael Fisher, Clare Dixon, Martin Peim
    Abstract:

    In this article, we examine how clausal resolution can be applied to a specific, but widely used, Nonclassical Logic, namely discrete linear temporal Logic. Thus, we first define a normal form for temporal formulae and show how arbitrary temporal formulae can be translated into the normal form, while preserving satisfiability. We then introduce novel resolution rules that can be applied to formulae in this normal form, provide a range of examples, and examine the correctness and complexity of this approach. Finally, we describe related work and future developments concerning this work.

Peimmartin - One of the best experts on this subject based on the ideXlab platform.

  • Clausal temporal resolution
    2020
    Co-Authors: Fishermichael, Dixonclare, Peimmartin
    Abstract:

    In this article, we examine how clausal resolution can be applied to a specific, but widely used, Nonclassical Logic, namely discrete linear temporal Logic. Thus, we first define a normal form for ...