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  1. (1 other version)Some theorems about the sentential calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
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  • (1 other version)Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke - 1963 - In Michael Dummett & J. N. Crossley (eds.), Formal Systems and Recursive Functions. Amsterdam,: North Holland. pp. 92-130.
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  • (1 other version)Propositional quantifiers in modal logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
    In this paper I shall present some of the results I have obtained on modal theories which contain quantifiers for propositions. The paper is in two parts: in the first part I consider theories whose non-quantificational part is S5; in the second part I consider theories whose non-quantificational part is weaker than or not contained in S5. Unless otherwise stated, each theory has the same language L. This consists of a countable set V of propositional variables pl, pa, ... , (...)
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  • Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
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  • Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1981 - Dordrecht, Netherland: Reidel.
    From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...)
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  • (1 other version)Some Theorems About the Sentential Calculi of Lewis and Heyting.J. C. C. Mckinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (3):171-172.
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  • (1 other version)Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Journal of Symbolic Logic 38 (2):329-329.
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  • (1 other version)Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke, J. N. Crossley & M. A. E. Dummett - 1970 - Journal of Symbolic Logic 35 (2):330-332.
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  • On the complexity of propositional quantification in intuitionistic logic.Philip Kremer - 1997 - Journal of Symbolic Logic 62 (2):529-544.
    We define a propositionally quantified intuitionistic logic Hπ + by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π +, S4π +, S4.2π +, K4π +, Tπ +, Kπ + and Bπ +, studied by Fine.
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  • Quantifying over propositions in relevance logic: nonaxiomatisability of primary interpretations of ∀ p and ∃ p.Philip Kremer - 1993 - Journal of Symbolic Logic 58 (1):334-349.
    A typical approach to semantics for relevance (and other) logics: specify a class of algebraic structures and take amodelto be one of these structures, α, together with some function or relation which associates with every formulaAa subset ofα. (This is the approach of, among others, Urquhart, Routley and Meyer and Fine.) In some cases there are restrictions on the class of subsets of α with which a formula can be associated: for example, in the semantics of Routley and Meyer [1973], (...)
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  • Compact propositional Gödel logics.Matthias Baaz & Richard Zach - 1998 - In Baaz Matthias (ed.), 28th IEEE International Symposium on Multiple-Valued Logic, 1998. Proceedings. IEEE Press. pp. 108-113.
    Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.
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  • Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Voronkov Andrei & Parigot Michel (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Springer. pp. 240-256.
    It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.
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