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  1.  32
    Full Classical S5 in Natural Deduction with Weak Normalization.Ana Teresa Martins & Lilia Ramalho Martins - 2008 - Annals of Pure and Applied Logic 152 (1):132-147.
    Natural deduction systems for classical, intuitionistic and modal logics were deeply investigated by Prawitz [D. Prawitz, Natural Deduction: A Proof-theoretical Study, in: Stockholm Studies in Philosophy, vol. 3, Almqvist and Wiksell, Stockholm, 1965. Reprinted at: Dover Publications, Dover Books on Mathematics, 2006] from a proof-theoretical perspective. Prawitz proved weak normalization for classical logic only for a language without logical or, there exists and with a restricted application of reduction ad absurdum. Reduction steps related to logical or, there exists and classical (...)
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  2.  10
    Expressiveness and Definability in Circumscription.Francicleber Martins Ferreira & Ana Teresa Martins - 2011 - Manuscrito 34 (1):233-266.
    We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is Δ-elementary, then it is elementary. That is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. This means that classes of (...)
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    On Minimal Models.Francicleber Ferreira & Ana Teresa Martins - 2007 - Logic Journal of the IGPL 15 (5-6):503-526.
    We investigate some logics which use the concept of minimal models in their definition. Minimal objects are widely used in Logic and Computer Science. They are applied in the context of Inductive Definitions, Logic Programming and Artificial Intelligence. An example of logic which uses this concept is the MIN logic due to van Benthem [20]. He shows that MIN is equivalent to the Least Fixed Point logic in expressive power. In [6], we extended MIN to the MIN Logic and proved (...)
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