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  1. Limits for Paraconsistent Calculi.Walter A. Carnielli & João Marcos - 1999 - Notre Dame Journal of Formal Logic 40 (3):375-390.
    This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...)
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  • Transfers between logics and their applications.M. E. Coniglio & W. A. Carnielli - 2002 - Studia Logica 72 (3):367-400.
    In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, (...)
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  • Contrapositionally complemented Heyting algebras and intuitionistic logic with minimal negation.Anuj Kumar More & Mohua Banerjee - 2023 - Logic Journal of the IGPL 31 (3):441-474.
    Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...)
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  • Intuitionistic Logic is a Connexive Logic.Davide Fazio, Antonio Ledda & Francesco Paoli - 2023 - Studia Logica 112 (1):95-139.
    We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ($$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: $$\textrm{CHL}$$ CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for $$\textrm{CHL}$$ CHL ; moreover, we (...)
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  • Conservative translations.Hércules A. Feitosa & Itala M. Loffredo D'Ottaviano - 2001 - Annals of Pure and Applied Logic 108 (1-3):205-227.
    In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations.
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  • Possible-translations semantics for some weak classically-based paraconsistent logics.João Marcos - 2008 - Journal of Applied Non-Classical Logics 18 (1):7-28.
    In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...)
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  • Volume I: Recovery operators in logics of formal inconsistency.Eduardo Alejandro Barrio & Walter Carnielli - 2020 - Logic Journal of the IGPL 28 (5):615-623.
    There are a considerable number of logics that do not seem to share the same inferential principles. Intuitionistic logics do not include the law of the exclude.
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  • What is a logic translation?Till Mossakowski, Răzvan Diaconescu & Andrzej Tarlecki - 2009 - Logica Universalis 3 (1):95-124.
    We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract (...)
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  • New dimensions on translations between logics.Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D’Ottaviano - 2009 - Logica Universalis 3 (1):1-18.
    After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
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