David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 49 (2):197 - 214 (1990)
We illustrate, with three examples, the interaction between boolean and modal connectives by looking at the role of truth-functional reasoning in the provision of completeness proofs for normal modal logics. The first example (§ 1) is of a logic (more accurately: range of logics) which is incomplete in the sense of being determined by no class of Kripke frames, where the incompleteness is entirely due to the lack of boolean negation amongst the underlying non-modal connectives. The second example (§ 2) focusses on the breakdown, in the absence of boolean disjunction, of the usual canonical model argument for the logic of dense Kripke frames, though a proof of incompleteness with respect to the Kripke semantics is not offered. An alternative semantic account is developed, in terms of which a completeness proof can be given, and this is used (§ 3) in the discussion of the third example, a bimodal logic which is, as with the first example, provably incomplete in terms of the Kripke semantics, the incompleteness being due to the lack of disjunction (as a primitive or defined boolean connective).
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References found in this work BETA
I. L. Humberstone (1985). The Formalities of Collective Omniscience. Philosophical Studies 48 (3):401 - 423.
David Makinson (1973). A Warning About the Choice of Primitive Operators in Modal Logic. Journal of Philosophical Logic 2 (2):193 - 196.
Dana Scott (1971). On Engendering an Illusion of Understanding. Journal of Philosophy 68 (21):787-807.
Krister Segerberg (1968). Decidability of S4. Theoria 34 (1):7-20.
Krister Segerberg (1967). Some Modal Logics Based on a Three-Valued Logic. Theoria 33 (1):53-71.
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