975 research outputs found
Automated Synthesis of Tableau Calculi
This paper presents a method for synthesising sound and complete tableau
calculi. Given a specification of the formal semantics of a logic, the method
generates a set of tableau inference rules that can then be used to reason
within the logic. The method guarantees that the generated rules form a
calculus which is sound and constructively complete. If the logic can be shown
to admit finite filtration with respect to a well-defined first-order semantics
then adding a general blocking mechanism provides a terminating tableau
calculus. The process of generating tableau rules can be completely automated
and produces, together with the blocking mechanism, an automated procedure for
generating tableau decision procedures. For illustration we show the
workability of the approach for a description logic with transitive roles and
propositional intuitionistic logic.Comment: 32 page
Hybrid type theory: a quartet in four movements
This paper sings a song -a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities (these can be found in Areces, Blackburn, Huertas, and Manzano [to appear]) rather it focusses on the underlying instruments, and the way they work together. We hope the reader will be tempted to sing along
Modal satisfiability via SMT solving
Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. Soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, AstronomÃa y FÃsica; Argentina.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina.Fil: Fontaine, Pascal. Université de Lorraine; Francia.Fil: Fontaine, Pascal. National Institute for Research in Digital Science and Technology; Francia.Fil: Merz, Stephan. Université de Lorraine; Francia.Fil: Merz, Stephan. National Institute for Research in Digital Science and Technology; Francia.Ciencias de la Computació
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