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  1. Extending Montague's System: A Three Valued Intensional Logic.E. H. Alves & J. A. D. Guerzoni - 1990 - Studia Logica 49 (1):127 - 132.
    In this note we present a three-valued intensional logic, which is an extension of both Montague's intensional logic and ukasiewicz three-valued logic. Our system is obtained by adapting Gallin's version of intensional logic (see Gallin, D., Intensional and Higher-order Modal Logic). Here we give only the necessary modifications to the latter. An acquaintance with Gallin's work is pressuposed.
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  • Completeness in Equational Hybrid Propositional Type Theory.Maria Manzano, Manuel Martins & Antonia Huertas - 2019 - Studia Logica 107 (6):1159-1198.
    Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order functional calculus (...)
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  • Completeness in Equational Hybrid Propositional Type Theory.Maria Manzano, Manuel Martins & Antonia Huertas - 2019 - Studia Logica 107 (6):1159-1198.
    Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order functional calculus (...)
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  • Identity, Equality, Nameability and Completeness. Part II.María Manzano & Manuel Crescencio Moreno - 2018 - Bulletin of the Section of Logic 47 (3):141.
    This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the (...)
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  • The Seven Virtues of Simple Type Theory.William M. Farmer - 2008 - Journal of Applied Logic 6 (3):267-286.
  • Supra-Logic: Using Transfinite Type Theory with Type Variables for Paraconsistency.Jørgen Villadsen - 2005 - Journal of Applied Non-Classical Logics 15 (1):45-58.
    We define the paraconsistent supra-logic Pσ by a type-shift from the booleans o of propositional logic Po to the supra-booleans σ of the propositional type logic P obtained as the propositional fragment of the transfinite type theory Q defined by Peter Andrews as a classical foundation of mathematics. The supra-logic is in a sense a propositional logic only, but since there is an infinite number of supra-booleans and arithmetical operations are available for this and other types, virtually anything can be (...)
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  • A Simple Type Theory with Partial Functions and subtypes11Supported by the MITRE-Sponsored Research Program. Presented at the 9th International Congress of Logic, Methodology and Philosophy of Science Held in Uppsala, Sweden, August 7-14, 1991. [REVIEW]William M. Farmer - 1993 - Annals of Pure and Applied Logic 64 (3):211-240.
    Simple type theory is a higher-order predicate logic for reasoning about truth values, individuals, and simply typed total functions. We present in this paper a version of simple type theory, called PF*, in which functions may be partial and types may have subtypes. We define both a Henkin-style general models semantics and an axiomatic system for PF*, and we prove that the axiomatic system is complete with respect to the general models semantics. We also define a notion of an interpretation (...)
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