The Experts below are selected from a list of 51 Experts worldwide ranked by ideXlab platform

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

  • Algorithmic correspondence and completeness in modal logic II. Polyadic and hybrid extensions of the algorithm SQEMA
    2016
    Co-Authors: Willem Conradie, Valentin Goranko
    Abstract:

    ABSTRACT. In [CON 06b] we introduced the algorithm SQEMA for computing first-order equiv-alents and proving canonicity of modal formulae, and thus established a very general cor-respondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. In this paper we develop several exten-sions of SQEMA where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension SemSQEMA we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon’s monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of SemSQEMA which guarantee canonicity, too

  • Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA
    Journal of Applied Logic, 2010
    Co-Authors: Willem Conradie, Valentin Goranko, Dimitar Vakarelov
    Abstract:

    In (CON 06b) we introduced the algorithmSQEMA for computing first-order equiv- alents and proving canonicity of modal formulae, and thus es tablished a very general cor- respondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a resul t by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. I this paper we develop several exten- sions of SQEMA where that syntactic condition is replaced by a semantic one , viz. downward monotonicity. For the first, and most general, extensionSemSQEMA we prove correctness for a large class of modal formulae containing an extension o the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a spe cial modal version of Lyndon's monotonicity theorem and imposing additional requirement s on the Ackermann rule we obtain restricted versions ofSemSQEMA which guarantee canonicity, too.

  • Algorithmic Correspondence and Completeness in Modal Logic
    Journal of Applied Non-Classical Logics, 2008
    Co-Authors: Willem Conradie, Valentin Goranko
    Abstract:

    In (Conradie et al., 2006a) we introduced the algorithm SQEMA for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. In this paper we develop several extensions of SQEMA where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension SemSQEMA we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versio...

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

  • Algorithmic correspondence and completeness in modal logic II. Polyadic and hybrid extensions of the algorithm SQEMA
    2016
    Co-Authors: Willem Conradie, Valentin Goranko
    Abstract:

    ABSTRACT. In [CON 06b] we introduced the algorithm SQEMA for computing first-order equiv-alents and proving canonicity of modal formulae, and thus established a very general cor-respondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. In this paper we develop several exten-sions of SQEMA where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension SemSQEMA we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon’s monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of SemSQEMA which guarantee canonicity, too

  • Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA
    Journal of Applied Logic, 2010
    Co-Authors: Willem Conradie, Valentin Goranko, Dimitar Vakarelov
    Abstract:

    In (CON 06b) we introduced the algorithmSQEMA for computing first-order equiv- alents and proving canonicity of modal formulae, and thus es tablished a very general cor- respondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a resul t by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. I this paper we develop several exten- sions of SQEMA where that syntactic condition is replaced by a semantic one , viz. downward monotonicity. For the first, and most general, extensionSemSQEMA we prove correctness for a large class of modal formulae containing an extension o the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a spe cial modal version of Lyndon's monotonicity theorem and imposing additional requirement s on the Ackermann rule we obtain restricted versions ofSemSQEMA which guarantee canonicity, too.

  • Algorithmic Correspondence and Completeness in Modal Logic
    Journal of Applied Non-Classical Logics, 2008
    Co-Authors: Willem Conradie, Valentin Goranko
    Abstract:

    In (Conradie et al., 2006a) we introduced the algorithm SQEMA for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. In this paper we develop several extensions of SQEMA where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension SemSQEMA we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versio...

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

  • Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA
    Journal of Applied Logic, 2010
    Co-Authors: Willem Conradie, Valentin Goranko, Dimitar Vakarelov
    Abstract:

    In (CON 06b) we introduced the algorithmSQEMA for computing first-order equiv- alents and proving canonicity of modal formulae, and thus es tablished a very general cor- respondence and canonical completeness result. SQEMA is based on transformation rules, the most important of which employs a modal version of a resul t by Ackermann that enables elimination of an existentially quantified Predicate Variable in a formula, provided a certain negative polarity condition on that Variable is satisfied. I this paper we develop several exten- sions of SQEMA where that syntactic condition is replaced by a semantic one , viz. downward monotonicity. For the first, and most general, extensionSemSQEMA we prove correctness for a large class of modal formulae containing an extension o the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a spe cial modal version of Lyndon's monotonicity theorem and imposing additional requirement s on the Ackermann rule we obtain restricted versions ofSemSQEMA which guarantee canonicity, too.

Rodrigo A. Freire - One of the best experts on this subject based on the ideXlab platform.

  • First-Order Logic and First-Order Functions
    Logica Universalis, 2015
    Co-Authors: Rodrigo A. Freire
    Abstract:

    This paper begins the study of first-order functions, which are a generalization of truth-functions. The concepts of truth-table and systems (and clones) of truth-functions, both introduced in propositional logic by Post, are also generalized and studied in the quantificational setting. The general facts about these concepts are given in the first five sections, and constitute a “general theory” of first-order functions. The central theme of this paper is the relation of definition among notions expressed by formulas of first-order logic. We emphasize that logic is not concerned only with the consequence relation among notions expressed by formulas. It also attends to the relation of definition among notions, where a notion is defined from other notions. Sections 5 and 6 deal exclusively with the relation of definition among notions expressed by formulas of first-order logic. In these sections, we study the systems of first-order functions, which are the sets of first-order functions closed under definitions. Sections 7 and 8 are concerned with the relativization of first-order functions to a class of structures. The relativization to a class of structures is a fundamental operation which is used in order to relate the theory of first-order functions with set theory and first-order model theory, a subject which we have barely scratched the surface. The apparatus developed in this paper enables us to define what is a vehicle for the foundation of classical mathematics in set theory, and, in Sect. 8, we prove that first-order logic with one binary Predicate Variable is not a minimal vehicle for the foundation of classical mathematics in set theory. Sections 9 and 10 introduce further operations and ideals of first-order functions. Besides some results on the influence of the arguments of a first-order function, a result about definability is proved in Sect. 10.1. It is this theorem that provides necessary and sufficient conditions for a first-order function to be in a finitely generated ideal. In Sect. 11, this result is applied to the problem of Predicate definability in classes of structures, the problem with which Beth’s theorem dealt in the case of elementary classes.

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

  • ON THE STRUCTURE OF Predicate NP1
    Studia Linguistica, 1993
    Co-Authors: Anders Holmberg
    Abstract:

    . The central hypothesis in this paper is that a Predicate NP is a maximal projection which is an open expression, meaning that it has an A-trace in its highest spec-position functioning as a Predicate Variable, while an argument NP is a closed expression, meaning that it has the head of an A-chain, usually pro in its highest spec-position. The distribution of articles, definite as well as indefinite, in combination with various attributes is explained largely as a consequence of licensing conditions on the highest spec-position and the categories it hosts. In addition some hitherto unnoticed facts concerning possessors in Predicate NPs are discussed.