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Carlos Caleiro [21]C. Caleiro [2]
  1. Two's Company: The humbug of many logical values.Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos - 2005 - In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic. Boston: Birkhäuser Verlog. 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.  27
    Axiomatizing non-deterministic many-valued generalized consequence relations.Sérgio Marcelino & Carlos Caleiro - 2019 - Synthese 198 (S22):5373-5390.
    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.  71
    What is a logical theory? On theories containing assertions and denials.Carolina Blasio, Carlos Caleiro & João Marcos - 2019 - Synthese 198 (S22):5481-5504.
    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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  4. Fibring non-truth-functional logics: Completeness preservation.C. Caleiro, W. A. Carnielli, M. E. Coniglio, A. Sernadas & C. Sernadas - 2003 - Journal of Logic, Language and Information 12 (2):183-211.
    Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...)
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  5.  6
    Modular Many-Valued Semantics for Combined Logics.Carlos Caleiro & Sérgio Marcelino - 2024 - Journal of Symbolic Logic 89 (2):583-636.
    We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics, whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics (...)
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  6. 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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  7.  9
    On Axioms and Rexpansions.Carlos Caleiro & Sérgio Marcelino - 2021 - In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Springer Verlag. pp. 39-69.
    We study the general problem of strengthening the logic of a given matrix with a set of axioms, using the idea of rexpansion. We obtain two characterization methods: a very general but not very effective one, and then an effective method which only applies under certain restrictions on the given semantics and the shape of the axioms. We show that this second method covers a myriad of examples in the literature. Finally, we illustrate how to obtain analytic multiple-conclusion calculi for (...)
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  8. 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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  9.  32
    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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  10.  67
    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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  11.  22
    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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  12.  36
    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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  13.  46
    (1 other version)Index of Authors of Volume 12.D. Ahn, G. Ben-Avi, D. Ben Shalom, Ph Besnard, K. Borthen, C. Caleiro, W. A. Carnielli, M. E. Coniglio, R. Cooper & N. Dimitri - 2003 - Journal of Logic, Language and Information 12 (531):531.
  14.  7
    Some More Theorems on Structural Entailment Relations and Non-deterministic Semantics.Carlos Caleiro, Sérgio Marcelino & Umberto Rivieccio - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 345-375.
    We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations—nowadays more commonly called multiple-conclusion logics—to the setting of non-deterministic matrices (Nmatrices), characterizing the Nmatrix models of an arbitrary logic through a generalization of the standard class operators to the non-deterministic setting. We highlight the main differences that appear in this more general setting, in particular: the possibility to obtain Nmatrix quotients using any compatible equivalence relation (not necessarily a congruence); the (...)
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  15.  21
    An Abstract Algebraic Logic Study of da Costa’s Logic and Some of its Paraconsistent Extensions.Hugo Albuquerque & Carlos Caleiro - 2022 - Bulletin of Symbolic Logic 28 (4):477-528.
    Two famous negative results about da Costa’s paraconsistent logic ${\mathscr {C}}_1$ (the failure of the Lindenbaum–Tarski process [44] and its non-algebraizability [39]) have placed ${\mathscr {C}}_1$ seemingly as an exception to the scope of Abstract Algebraic Logic (AAL). In this paper we undertake a thorough AAL study of da Costa’s logic ${\mathscr {C}}_1$. On the one hand, we strengthen the negative results about ${\mathscr {C}}_1$ by proving that it does not admit any algebraic semantics whatsoever in the sense of Blok (...)
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  16.  23
    Petrópolis, Rio de Janeiro, Brazil May 9–13, 2011.Carlos Areces, Carlos Caleiro & Gregory Chaitin - 2012 - Bulletin of Symbolic Logic 18 (1).
  17.  38
    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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  18.  39
    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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  19.  23
    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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  20. Plug and Play Negations.Umberto Rivieccio, Carlos Caleiro & Sérgio Marcelino - 2018 - In Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency. Cham, Switzerland: Springer.
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  21. 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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