Interactive Learning Based Realizability and 1-Backtracking Games
نویسندگان
چکیده
منابع مشابه
Interactive Learning Based Realizability and 1-Backtracking Games
We prove that interactive learning based classical realizability (introduced by Aschieri and Berardi for first order arithmetic [1]) is sound with respect to 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 realizer and winnin...
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We prove a soundness and completeness result for Aschieri and Berardi’s 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 1Backtracking Coquand game semantics. In particular, any realizer of an implication-and-neg...
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We associate to any game G, in the sense of Set Theory, a variant of it we call bck(G). We show through examples that many relevant non-constructive proofs in Algebra and Combinatorics can be interpreted by recursive winning strategy over some game of the form bck(G). We further support this claim by proving that games of the form bck(G) are a sound and complete semantic for a sub-classical log...
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We apply to the semantics of Arithmetic the idea of “finite approximation” used to provide computational interpretations of Herbrand’s Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for ∨, ∃) over a suitable structure N for the language of natural numbers and maps of Gödel’s system T . We introduce a new Realizability semantics we call “Interactive le...
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In this dissertation we collect some results about “interactive realizability”, a realizability semantics that extends the Brouwer-Heyting-Kolmogorov interpretation to (sub-)classical logic, more precisely to first-order intuitionistic arithmetic (Heyting Arithmetic, HA) extended by the law of the excluded middle restricted to Σ1 formulas (EM1), a system motivated by its interest in proof minin...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2011
ISSN: 2075-2180
DOI: 10.4204/eptcs.47.3