Abstract
A great deal of research has been done on Heyting’s propositional calculus and on intermediate logics, logics between Heyting’s propositional calculus, h, and the classical propositional calculus, c. In this chapter we shall
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(a)
study the correspondence between axioms added to h and geometrical conditions on the Kripke structures
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(b)
introduce special methods, such as selective filtration, to study certain intermediate logics.
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Notes
In writing this Chapter I used profitably C. Smorynski’s thesis. The idea of filtration was first introduced in modal logic by E. J. Lemmon and D. Scott, 1966. K. Segerberg introduced it in Kripke structures and developed the method further. The author continued with it, calling the refined form selective filtration.
Incomparable intermediate logics were given independently by Jankov, 1968 and K. Fine. We base our presentation here on Fine’s results. The fragment without y was studied by A. Diego. We base our presentation on A. Urquhart. We also use results of K. Segerberg, 1974.
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© 1981 Springer Science+Business Media Dordrecht
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Gabbay, D.M. (1981). Heyting’s Propositional Calculus and Extensions. In: Semantical Investigations in Heyting’s Intuitionistic Logic. Synthese Library, vol 148. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2977-2_5
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DOI: https://doi.org/10.1007/978-94-017-2977-2_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8362-3
Online ISBN: 978-94-017-2977-2
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