CALEIRO AND RICARDO GONÇALVES , Behavioral

Cn Systems of da Costa. SQIG-Instituto de Telecomunicações and Department of Mathematics, IST, TU Lisbon, Portugal. E-mail: [email protected]. It is well known that the paraconsistent logics Cn of da Costa fail to be algebraizable [1, 4]. Even so, an algebraic counterpart for them has been proposed in the literature, namely the class of da Costa algebras [2, 3]. Still, the connection between this proposal and Cn was never established at the light of the theory of algebraization of logics as introduced in [7]. In this work, we propose to use the tools and techniques of the novel theory of Behavioral Abstract Algebraic Logic, as introduced in [5], to study the Cn systems from an algebraic point of view and ultimately obtain a precise characterization of their relationship to da Costa algebras. As a side-effect, the algebraic nature of its bivaluation semantics [6] is also clarified. This work was partially supported by FCT and EU FEDER, namely via the QuantLog POCI/MAT/55796/2004 and KLog PTDC/MAT/68723/2006 projects of SQIG-IT. The second author was also supported by FCT under the PhD grant SFRH/BD/18345/2004/SV7T. [1] R. Lewin and I. Mikenberg and M. Schwarze, C1 is not algebraizable, Notre Dame Journal of Formal Logic, volume 32, number 4, 1991, 609–611. [2] N. C. A. da Costa, Opérations non monotones dans les treillis, Comptes Rendus de l’Academie de Sciences de Paris, number 263, 1966, A423–A429. [3] W. A. Carnielli and L. P. de Alcantara, Paraconsistent Algebras, Studia Logica, number 43, 1984, 79–88. [4] C. Mortensen, Every quotient algebra for C1 is trivial, Notre Dame Journal of Formal Logic, volume 21, 1980, 694–700. [5] C. Caleiro and R. Gonçalves and M. Martins, Behavioral Abstract Algebraic Logic, Submitted for publication, 2007. [6] N. da Costa and E. Alves A semantical analysis of the calculi Cn, Notre Dame Journal of Formal Logic, volume 18, number 4, 1977, 621–630. [7] W. Blok and D. Pigozzi, Algebraizable Logics, Memoirs of the AMS, volume 77, number 396, 1989. URL: http://www.math.ist.utl.pt/∼rgon