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  1. A Simple Logic of Functional Dependence.Alexandru Baltag & Johan van Benthem - 2021 - Journal of Philosophical Logic 50 (5):939-1005.
    This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous (...)
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  • (1 other version)Substitutions of< i> Σ_< sub> 1< sup> 0-sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic. [REVIEW]Albert Visser - 2002 - Annals of Pure and Applied Logic 114 (1):227-271.
    This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...)
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  • (1 other version)Substitutions of Σ10-sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic.Albert Visser - 2002 - Annals of Pure and Applied Logic 114 (1-3):227-271.
    This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...)
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  • Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick de Jongh - 2012 - Studia Logica 100 (1):61-89.
    We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n-universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.
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  • Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick Jongh - 2012 - Studia Logica 100 (1-2):61-89.
    We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n -universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.
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  • Logical relations.Lloyd Humberstone - 2013 - Philosophical Perspectives 27 (1):175-230.
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  • Classically archetypal rules.Tomasz Połacik & Lloyd Humberstone - 2018 - Review of Symbolic Logic 11 (2):279-294.
    A one-premiss rule is said to be archetypal for a consequence relation when not only is the conclusion of any application of the rule a consequence of the premiss, but whenever one formula has another as a consequence, these formulas are respectively equivalent to a premiss and a conclusion of some application of the rule. We are concerned here with the consequence relation of classical propositional logic and with the task of extending the above notion of archetypality to rules with (...)
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