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Satisfiability Calculus: The Semantic Counterpart of a Proof Calculus in General Logics

  • Carlos Gustavo López Pombo
  • Pablo F. Castro
  • Nazareno M. Aguirre
  • Thomas S. E. Maibaum
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7841)

Abstract

Since its introduction by Goguen and Burstall in 1984, the theory of institutions has been one of the most widely accepted formalizations of abstract model theory. This work was extended by a number of researchers, José Meseguer among them, who presented General Logics, an abstract framework that complements the model theoretical view of institutions by defining the categorical structures that provide a proof theory for any given logic. In this paper we intend to complete this picture by providing the notion of Satisfiability Calculus, which might be thought of as the semantical counterpart of the notion of proof calculus, that provides the formal foundations for those proof systems that use model construction techniques to prove or disprove a given formula, thus “implementing” the satisfiability relation of an institution.

Keywords

Modal Logic Natural Transformation Logical System Proof Theory Kripke Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© IFIP International Federation for Information Processing 2013

Authors and Affiliations

  • Carlos Gustavo López Pombo
    • 1
    • 3
  • Pablo F. Castro
    • 2
    • 3
  • Nazareno M. Aguirre
    • 2
    • 3
  • Thomas S. E. Maibaum
    • 4
  1. 1.Departmento de Computación, FCEyNUniversidad de Buenos AiresArgentina
  2. 2.Departmento de Computación, FCEFQyNUniversidad Nacional de Río CuartoArgentina
  3. 3.Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)Argentina
  4. 4.Department of Computing & SoftwareMcMaster UniversityCanada

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