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

Carlos Gustavo López Pombo, Pablo F. Castro, Nazareno M. Aguirre, Thomas S. E. Maibaum
2013 Lecture Notes in Computer Science  
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
more » ... ng 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. N. Martí-Oliet and M. Palomino (Eds.): WADT 2012, LNCS 7841, pp. 195-211, 2013. c IFIP International Federation for Information Processing 2013 1 Authors' note: Meseguer refers to a logic as a structure that is composed of an entailment system together with an institution, see Def. 6.
doi:10.1007/978-3-642-37635-1_12 fatcat:c367lec4pbglzlf7dji2o6edyq