Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator. Part II

This paper is a continuation of Inou´e [5]. As already mentioned in the paper, a number of intuitionistic provable formulas are given with a Hilbert-style proof. For that, we make use of a family of intuitionistic deduction theorems, which are also presented in this paper by means of Mizar system [2], [1]. Our axiom system of intuitionistic propositional logic IPC is based on the propositional subsystem of H1-IQC in Troelstra and van Dalen [6, p. 68]. We also owe Heyting [4] and van Dalen [7]. Our treatment of a set-theoretic intuitionistic deduction theorem is due to Agata Darmochwał’s Mizar article “Calculus of Quantifiers. Deduction Theorem” [3].Takao Inoué - Department of Medical Molecular Informatics, Meiji Pharmaceutical University, Tokyo, Japan; Graduate School of Science and Engineering, Hosei University, Tokyo, Japan; Department of Applied Informatics, Faculty of Science and Engineering, Hosei University, Tokyo, JapanRiku Hanaoka - Keyaki-Sou 403, Midori-cho 5-17-27, Koganei-city, 184-0003, Tokyo, JapanGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-817.Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.Agata Darmochwał. Calculus of quantifiers. Deduction theorem. Formalized Mathematics, 2(2):309–312, 1991.Arend Heyting. Intuitionism. An introduction. Elsevier, Amsterdam, 3rd revised ed., 1971.Takao Inoué. Intuitionistic propositional calculus in the extended framework with modal operator. Part I. Formalized Mathematics, 11(3):259–266, 2003.Anne Sjerp Troelstra and Dirk van Dalen. Constructivism in mathematics. An introduction. Volume I, volume 121 of Studies in Logic and the Foundations of Mathematics. Amsterdam etc.: North-Holland, 1988. ISBN 0-444-70506-6.Dirk van Dalen. Logic and Structure. London: Springer, 2013. ISBN 978-1-4471-4557-8; 978-1-4471-4558-5. doi:10.1007/978-1-4471-4558-5.30111

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm