9 found
Order:
Disambiguations
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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  2.  49
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  3. Flexibly Structured Predication.Barry Taylor & Allen P. Hazen - 1992 - Logique Et Analyse 35:374-393.
  4.  40
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  11
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  50
    Against Cantorism.Allen P. Hazen - 1994 - Sophia 33 (2):21-32.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7. Some Lessons Learned About Adding Conditionals to Certain Many-Valued Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2022 - 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.
    Direct download  
     
    Export citation  
     
    Bookmark  
  8.  8
    Platonismo E convenzioni.Allen P. Hazen - 2009 - Rivista di Estetica 41:171-187.
    Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  9. Russell, Gödel and Skolem: How Much of Arithmetic is Predicative.Jen M. Davoren & Allen P. Hazen - 1991 - Journal of Symbolic Logic 56:1108-1109.