Implementation of propositional temporal logics using BDDs

This tutorial intends to convey the step-by-step process by which computer programs for model checking and satisfiability testing for temporal logics may be derived from the theory. The idea is to demonstrate that it is very well possible to implement such a program in an efficient way without sacrificing a correct-by-construction approach. The tutorial will be fully self-contained, only a general knowledge of programming and propositional logic is assumed

Satisfiability for relation-changing logics

Relation-changing modal logics (RC for short) are extensions of the basic modal logic with dynamic operators that modify the accessibility relation of a model during the evaluation of a formula. These languages are equipped with dynamic modalities that are able e.g. to delete, add and swap edges in the model, both locally and globally. We study the satisfiability problem for some of these logics.We first show that they can be translated into hybrid logic. As a result, we can transfer some results from hybrid logics to RC. We discuss in particular decidability for some fragments. We then show that satisfiability is, in general, undecidable for all the languages introduced, via translations from memory logics.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martel, Mauricio. Universitat Bremen; Alemani

SCL(EQ): SCL for First-Order Logic with Equality

We propose a new calculus SCL(EQ) for first-order logic with equality thatonly learns non-redundant clauses. Following the idea of CDCL (Conflict DrivenClause Learning) and SCL (Clause Learning from Simple Models) a ground literalmodel assumption is used to guide inferences that are then guaranteed to benon-redundant. Redundancy is defined with respect to a dynamically changingordering derived from the ground literal model assumption. We prove SCL(EQ)sound and complete and provide examples where our calculus improves onsuperposition.<br

SCL: Clause Learning from Simple Models

International audienceSeveral decision procedures for the Bernays-Schoenfinkel (BS) fragment of first-order logic rely on explicit model assumptions. In particular, the procedures differ in their respective model representation formalisms. We introduce a new decision procedure SCL deciding the BS fragment. SCL stands for clause learning from simple models. Simple models are solely built on ground literals. Nevertheless, we show that SCL can learn exactly the clauses other procedures learn with respect to more complex model representation formalisms. Therefore, the overhead of complex model representation formalisms is not always needed. SCL is sound and complete for full first-order logic without equality

Certificates for decision problems in temporal logic using context-based tableaux and sequent calculi.

115 p.Esta tesis trata de resolver problemas de Satisfactibilidad y Model Checking, aportando certificados del resultado. En ella, se trabaja con tres lógicas temporales: Propositional Linear Temporal Logic (PLTL), Computation Tree Logic (CTL) y Extended Computation Tree Logic (ECTL). Primero se presenta el trabajo realizado sobre Certified Satisfiability. Ahí se muestra una adaptación del ya existente método dual de tableaux y secuentes basados en contexto para satisfactibilidad de fórmulas PLTL en Negation Normal Form. Se ha trabajado la generación de certificados en el caso en el que las fórmulas son insactisfactibles. Por último, se aporta una prueba de soundness del método. Segundo, se ha optimizado con Sat Solvers el método de Certified Satisfiability para el contexto de Certified Model Checking. Se aportan varios ejemplos de sistemas y propiedades. Tercero, se ha creado un nuevo método dual de tableaux y secuentes basados en contexto para realizar Certified Satisfiability para fórmulas CTL yECTL. Se presenta el método y un algoritmo que genera tanto el modelo en el caso de que las fórmulas son satisfactibles como la prueba en el caso en que no lo sean. Por último, se presenta una implementación del método para CTL y una experimentación comparando el método propuesto con otro método de similares características