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  1. Logic may be simple. Logic, congruence and algebra.Jean-Yves Béziau - 1997 - Logic and Logical Philosophy 5:129-147.
    This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these concepts are related to such notions as (...)
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  • From Curry to Haskell.Felice Cardone - 2020 - Philosophy and Technology 34 (1):57-74.
    We expose some basic elements of a style of programming supported by functional languages like Haskell by relating them to a coherent set of notions and techniques from Curry’s work in combinatory logic and formal systems, and their algebraic and categorical interpretations. Our account takes the form of a commentary to a simple fragment of Haskell code attempting to isolate the conceptual sources of the linguistic abstractions involved.
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  • Principal type-schemes and condensed detachment.J. Roger Hindley & David Meredith - 1990 - Journal of Symbolic Logic 55 (1):90-105.
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  • Prelogic of logoi.Marcel Crabbé - 1976 - Studia Logica 35 (3):219 - 226.
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  • Idempotent Full Paraconsistent Negations are not Algebraizable.Jean- Yves Beziau - unknown
    1 What are the features of a paraconsistent negation? Since paraconsistent logic was launched by da Costa in his seminal paper [4], one of the fundamental problems has been to determine what exactly are the theoretical or metatheoretical properties of classical negation that can have a unary operator not obeying the principle of noncontradiction, that is, a paraconsistent operator. What the result presented here shows is that some of these properties are not compatible with each other, so that in constructing (...)
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  • Idempotent Full Paraconsistent Negations are not Algebraizable.Jean-Yves Béziau - 1998 - Notre Dame Journal of Formal Logic 39 (1):135-139.
    Using methods of abstract logic and the theory of valuation, we prove that there is no paraconsistent negation obeying the law of double negation and such that $\neg(a\wedge\neg a)$ is a theorem which can be algebraized by a technique similar to the Tarski-Lindenbaum technique.
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