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Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants

Rohan French

Notre Dame Journal of Formal Logic 53 (4):549-556 (2012)

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A Unified Semantics for a Family of Modal Logics with Propositional Constants.Matteo Pascucci - 2016 - Logica Universalis 10 (1):45-66.details This article concerns the metatheory of a class of modal logics whose language includes propositional constants of various kinds. The main novelties are the use of general frames with specific restrictions and the definition of the strict range of a formula. Many examples from the literature are treated within the framework provided and some traditional model-theoretic issues such as preservation results concerning the validity of formulas and definability results concerning frame properties are addressed. Download Export citation Bookmark
Note on Extending Congruential Modal Logics.Lloyd Humberstone - 2016 - Notre Dame Journal of Formal Logic 57 (1):95-103.details It is observed that a consistent congruential modal logic is not guaranteed to have a consistent extension in which the Box operator becomes a truth-functional connective for one of the four one-place truth functions. Download Export citation Bookmark 4 citations
An observation concerning porte's rule in modal logic.Rohan French & Lloyd Humberstone - 2015 - Bulletin of the Section of Logic 44 (1/2):25-31.details It is well known that no consistent normal modal logic contains (as theorems) both ♦A and ♦¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ♦A, or else no consistent normal modal logic contains ♦¬A. Download Export citation Bookmark
(1 other version)The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2012 - Journal of Philosophical Logic (1):1-20.details Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...) Download Export citation Bookmark 8 citations
(1 other version)The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2014 - Journal of Philosophical Logic 43 (1):133-152.details Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...) Download Export citation Bookmark 8 citations

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