Abstract
We show that the uniform validity is equivalent to the non-uniform validity for both Blass’ semantics of [1] and Japaridze’s semantics of [5] (thus proving a conjecture from [5]). We present a shorter proof (than that of [10]) of the completeness of the positive fragment of intuitionistic logic for both these semantics. Finally, we show that validity for the “parallel recurrence” version of Japaridze’s semantics of [5] is equivalent to accomplishability in the sense of [4].
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Mezhirov, I., Vereshchagin, N. (2008). On Game Semantics of the Affine and Intuitionistic Logics. In: Hodges, W., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2008. Lecture Notes in Computer Science(), vol 5110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69937-8_4
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DOI: https://doi.org/10.1007/978-3-540-69937-8_4
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