5 found
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Newton M. Peron [4]Newton Marques Peron [1]
  1.  29
    Finite Non-Deterministic Semantics for Some Modal Systems.Marcelo E. Coniglio, Luis Fariñas del Cerro & Newton M. Peron - 2015 - Journal of Applied Non-Classical Logics 25 (1):20-45.
    Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of the paper (...)
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  2.  12
    Dugundji’s Theorem Revisited.Marcelo E. Coniglio & Newton M. Peron - 2014 - Logica Universalis 8 (3-4):407-422.
    In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal logic (...)
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  3.  55
    Modal Extensions of Sub-Classical Logics for Recovering Classical Logic.Marcelo E. Coniglio & Newton M. Peron - 2013 - Logica Universalis 7 (1):71-86.
    In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to (...)
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  4.  22
    Errata and Addenda to ‘Finite Non-Deterministic Semantics for Some Modal Systems’.Marcelo E. Coniglio, Luis Fariñas del Cerro & Newton M. Peron - 2016 - Journal of Applied Non-Classical Logics 26 (4):336-345.
    In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...)
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  5.  70
    A Paraconsistentist Approach to Chisholm's Paradox.Marcelo Esteban Coniglio & Newton Marques Peron - 2009 - Principia: An International Journal of Epistemology 13 (3):299-326.
    The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do (...)
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