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  1. Learning based realizability for HA + EM1 and 1-Backtracking games: Soundness and completeness.Federico Aschieri - 2013 - Annals of Pure and Applied Logic 164 (6):591-617.
    We prove a soundness and completeness result for Aschieri and Berardiʼs learning based realizability for Heyting Arithmetic plus Excluded Middle over semi-decidable statements with respect to 1-Backtracking Coquand game semantics. First, we prove that learning based realizability is sound with respect to 1-Backtracking Coquand game semantics. In particular, any realizer of an implication-and-negation-free arithmetical formula embodies a winning recursive strategy for the 1-Backtracking version of Tarski games. We also give examples of realizers and winning strategy extraction for some classical proofs. (...)
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  • Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research.Yaroslav Shramko - 2005 - Studia Logica 80 (2-3):347-367.
    We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to (...)
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  • Bi-Heyting algebras, toposes and modalities.Gonzalo E. Reyes & Houman Zolfaghari - 1996 - Journal of Philosophical Logic 25 (1):25 - 43.
    The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs.
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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
  • Meaning and proofs: On the conflict between classical and intuitionistic logic.Dag Prawitz - 1977 - Theoria 43 (1):2--40.
  • A constructivism based on classical truth.Pierangelo Miglioli, Ugo Moscato, Mario Ornaghi & Gabriele Usberti - 1988 - Notre Dame Journal of Formal Logic 30 (1):67-90.
  • 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.
  • Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
  • A pragmatic interpretation of intuitionistic propositional logic.Carlo Dalla Pozza & Claudio Garola - 1995 - Erkenntnis 43 (1):81-109.
    We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...)
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  • The techniques of disputation in the history of logic.Ignacio Angelelli - 1970 - Journal of Philosophy 67 (20):800-815.