Examinando por Materia "Formal logic"

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    Combining interactive and automatic reasoning in first order theories of functional programs
    (SPRINGER, 2012-01-01) Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    We propose a new approach to the computer-assisted verification of functional programs. We work in first order theories of functional programs which are obtained by extending Aczel's first order theory of combinatory formal arithmetic with positive inductive and coinductive predicates. Rather than building a special purpose system we implement our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by encoding first order theories using the formulae-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first order logic which can be called by a program which translates Agda representations of first order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proof by induction and coinduction. © 2012 Springer-Verlag Berlin Heidelberg.
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    Restricted normal modal logics and levelled possible worlds semantics
    (OXFORD UNIV PRESS, 2014-08-01) Agudelo-Agudelo, Juan C.; Sierra-Aristizabal, Manuel H.; Agudelo-Agudelo, Juan C.; Sierra-Aristizabal, Manuel H.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    Restricted normal modal logics are here defined by imposing conditions on the modal axioms and rules of normal modal systems. The conditions are defined in terms of a depth (associated with the modal connective) and a complexity function. It is proven that the logics obtained are characterized by a subtle adaptation of the possible worlds semantics in which levels are associated with the worlds. Restricted normal modal logics constitute a general framework allowing the definition of a huge variety of modal systems, which can have different applications. For instance, they are useful to define epistemic logics where the logical omniscience problem is partially controlled. © 2014 The Author.