16 found
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  1. Two's Company: The Humbug of Many Logical Values.Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos - 2005 - In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlag. pp. 169-189.
    The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more (...)
     
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  2.  8
    Axiomatizing Non-Deterministic Many-Valued Generalized Consequence Relations.Sérgio Marcelino & Carlos Caleiro - forthcoming - Synthese:1-18.
    We discuss the axiomatization of generalized consequence relations determined by non-deterministic matrices. We show that, under reasonable expressiveness requirements, simple axiomatizations can always be obtained, using inference rules which can have more than one conclusion. Further, when the non-deterministic matrices are finite we obtain finite axiomatizations with a suitable generalized subformula property.
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  3.  74
    Behavioral Algebraization of Logics.Carlos Caleiro, Ricardo Gonçalves & Manuel Martins - 2009 - Studia Logica 91 (1):63-111.
    We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new (...)
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  4.  91
    From Fibring to Cryptofibring. A Solution to the Collapsing Problem.Carlos Caleiro & Jaime Ramos - 2007 - Logica Universalis 1 (1):71-92.
    . The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For (...)
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  5.  24
    Decidability and Complexity of Fibred Logics Without Shared Connectives.Sérgio Marcelino & Carlos Caleiro - 2016 - Logic Journal of the IGPL 24 (5).
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  6.  8
    Hierarchical Logical Consequence.Carlos Caleiro, Paula Gouveia & Jaime Ramos - 2011 - Logic Journal of the IGPL 19 (4):544-565.
    The modern view of logical reasoning as modeled by a consequence operator has allowed for huge developments in the study of logic as an abstract discipline. Still, it is unable to explain why it is often the case that the same designation is used, in an ambiguous way, to describe several distinct modes of reasoning over the same logical language. A paradigmatic example of such a situation is ‘modal logic’, a terminology which can encompass reasoning over Kripke frames, but also (...)
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  7.  37
    Synchronization of Logics.Amílcar Sernadas, Cristina Sernadas & Carlos Caleiro - 1997 - Studia Logica 59 (2):217-247.
    Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction (...)
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  8.  10
    Behavioral Algebraization of da Costa's C-Systems.Carlos Caleiro & Ricardo Gonçalves - 2009 - Journal of Applied Non-Classical Logics 19 (2):127-148.
    It is well-known that da Costa's C-systems of paraconsistent logic do not admit a Blok-Pigozzi algebraization. Still, an algebraic flavored semantics for them has been proposed in the literature, namely using the class of so-called da Costa algebras. However, the precise connection between these semantic structures and the C-systems was never established at the light of the theory of algebraizable logics. In this paper we propose to study the C-systems from an algebraic point of view, and to fill in this (...)
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  9.  10
    Petrópolis, Rio de Janeiro, Brazil May 9–13, 2011.Carlos Areces, Carlos Caleiro & Gregory Chaitin - 2012 - Bulletin of Symbolic Logic 18 (1).
  10.  24
    What is a Logical Theory? On Theories Containing Assertions and Denials.Carolina Blasio, Carlos Caleiro & João Marcos - forthcoming - Synthese:1-24.
    The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by (...)
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  11.  26
    Abstract Valuation Semantics.Carlos Caleiro & Ricardo Gonçalves - 2013 - Studia Logica 101 (4):677-712.
    We define and study abstract valuation semantics for logics, an algebraically well-behaved version of valuation semantics. Then, in the context of the behavioral approach to the algebraization of logics, we show, by means of meaningful bridge theorems and application examples, that abstract valuations are suited to play a role similar to the one played by logical matrices in the traditional approach to algebraization.
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  12.  22
    Compositional Meaning in Logic.Carlos Caleiro & Luca Viganò - 2017 - Logica Universalis 11 (3):283-295.
    The Fregean-inspired Principle of Compositionality of Meaning for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the domain of (...)
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  13.  64
    On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW]Carlos Caleiro, Luca Viganò & Marco Volpe - 2013 - Logica Universalis 7 (1):33-69.
    We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...)
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  14.  4
    Relating Strand Spaces and Distributed Temporal Logic for Security Protocol Analysis.Carlos Caleiro, Luca Viganò & David Basin - 2005 - Logic Journal of the IGPL 13 (6):637-663.
    In previous work, we introduced a version of distributed temporal logic that is well-suited both for verifying security protocols and as a metalogic for reasoning about, and relating, different security protocol models. In this paper, we formally investigate the relationship between our approach and strand spaces, which is one of the most successful and widespread formalisms for analyzing security protocols. We define translations between models in our logic and strand-space models of security protocols, and we compare the results obtained with (...)
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  15.  6
    XIV Latin American Symposium on Mathematical Logic (SLALM)(Vol 15, Pg 332, 2009).Carlos Caleiro & Ricardo Goncalves - 2010 - Bulletin of Symbolic Logic 16 (1):332-376.
  16.  21
    16th Workshop on Logic, Language, Information and Computation (WoLLIC 2009).Hans Tompits, Ken Satoh, Arnold Beckmann, Carlos Caleiro, Thomas Eiter, Sylvain Salvati, Taisuke Sato & Frank Wolter - 2010 - Bulletin of Symbolic Logic 16 (1):805-815.