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  1. The Connectives.Lloyd Humberstone - 2011 - MIT Press.
    It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.This landmark work offers both ...
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  • Inquisitive Semantics.Ivano Ciardelli, Jeroen Groenendijk & Floris Roelofsen - 2018 - Oxford, England: Oxford University Press.
    The book presents a new logical framework to capture the meaning of sentences in conversation. It is based on a richer notion of meaning than traditional approaches, and allows for an integrated treatment of statements and questions. The first part of the book presents the framework in detail, while the second demonstrates its many benefits.
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  • Complexity of Intuitionistic Propositional Logic and its Fragments.Mikhail Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):267-292.
    In the paper we consider complexity of intuitionistic propositional logic and its natural fragments such as implicative fragment, finite-variable fragments, and some others. Most facts we mention here are known and obtained by logicians from different countries and in different time since 1920s; we present these results together to see the whole picture.
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  • Weak Negation in Inquisitive Semantics.Vít Punčochář - 2015 - Journal of Logic, Language and Information 24 (3):323-355.
    This paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The main result (...)
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  • Compatible Functions in Algebras Associated to Extensions of Positive Logic.Rodolfo Ertola, Adriana Galli & Marta Sagastuma - 2007 - Logic Journal of the IGPL 15 (1):109-119.
    In [4], Caicedo and Cignoli study compatible functions on Heyting algebras and the corresponding logical properties of connectives defined on intuitionistic propositional calculus. In this paper we study some aspects of compatible functions on the algebras associated to positive propositional calculus and successive extensions of it: intuitionistic calculus itself, the modal symmetric propositional calculus of Moisil and n-valued Łukasiewicz propositional calculus.
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  • Lattice Theory.Garrett Birkhoff - 1950 - Journal of Symbolic Logic 15 (1):59-60.
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  • Is Even Minimal Negation Constructive?A. P. Hazen - 1995 - Analysis 55 (2):105 - 107.
  • On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic.Andrew M. Pitts - 1992 - Journal of Symbolic Logic 57 (1):33-52.
    We prove the following surprising property of Heyting's intuitionistic propositional calculus, IpC. Consider the collection of formulas, φ, built up from propositional variables (p,q,r,...) and falsity $(\perp)$ using conjunction $(\wedge)$ , disjunction (∨) and implication (→). Write $\vdash\phi$ to indicate that such a formula is intuitionistically valid. We show that for each variable p and formula φ there exists a formula Apφ (effectively computable from φ), containing only variables not equal to p which occur in φ, and such that for (...)
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  • An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  • Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
  • On the Principle of the Excluded Middle.Andrei Kolomogorov - 1925 - In ¸ Itevanheijenoort1967. Harvard University Press. pp. 416-437.
     
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  • Subminimal Logic and Weak Algebras.Rodolfo Ertola & Marta Sagastume - 2009 - Reports on Mathematical Logic:153-166.
    n this paper we investigate the implication-less fragment of Johansson's minimal logic. We call it subminimal logic and we study its associated algebras, which we call weak algebras. We prove the algebraic Glivenko theorem, soundness and completeness for this logic.
     
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