9 found
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Allen P. Hazen [9]Allen Patterson Hazen [1]
  1. Actuality in Propositional Modal Logic.Allen P. Hazen, Benjamin G. Rin & Kai F. Wehmeier - 2013 - Studia Logica 101 (3):487-503.
    We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality (...)
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  2.  80
    Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...)
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  3.  68
    Second-Order Logic of Paradox.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Notre Dame Journal of Formal Logic 59 (4):547-558.
    The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding that it will be extremely (...)
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  4. Flexibly structured predication.Barry Taylor & Allen P. Hazen - 1992 - Logique Et Analyse 35:374-393.
  5.  35
    Pecularities of Some Three- and Four-Valued Second Order Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Logica Universalis 12 (3-4):493-509.
    Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...)
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  6. Russell, Gödel and Skolem: how much of arithmetic is predicative.Jen M. Davoren & Allen P. Hazen - 1991 - Journal of Symbolic Logic 56:1108-1109.
  7.  69
    Against cantorism.Allen P. Hazen - 1994 - Sophia 33 (2):21-32.
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  8.  19
    Platonismo e Convenzioni.Allen P. Hazen - 2009 - Rivista di Estetica 41:171-187.
    Il platonista sostiene che le verità della matematica e della logica siano letteralmente vere, ossia che descrivano (in qualche modo: non voglio legare la definizione a una particolare teoria semantica) realtà che non sono create o decise da noi. Il convenzionalista sostiene invece che le proposizioni che chiamiamo verità della matematica siano in qualche misura convenzionali: esse esprimerebbero convenzioni che abbiamo adottato noi, o certe loro conseguenze. Le due posizioni sono apparenteme...
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  9.  21
    Some Lessons Learned About Adding Conditionals to Certain Many-Valued Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2021 - In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 557-570.
    There are good reasons to want logics, including many-valued logics, to have usable conditionals, and we have explored this in certain logics. However, it turns out that we “accidentally” chose some favourable logics. In this paper, we look at some of the unfavourable logics and describe where usable conditionals can be added and where it is not possible.
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