David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
S. K. Thomason (1972). Semantic Analysis of Tense Logics. Journal of Symbolic Logic 37 (1):150-158.
Dana Scott (1971). On Engendering an Illusion of Understanding. Journal of Philosophy 68 (21):787-807.
Krister Segerberg (1968). Propositional Logics Related to Heyting's and Johansson's. Theoria 34 (1):26-61.
Krister Segerberg (1968). Decidability of S4. Theoria 34 (1):7-20.
Krister Segerberg (1967). On the Logic of “To-Morrow”. Theoria 33 (1):45-52.
Citations of this work BETA
Lloyd Humberstone (2005). For Want of an 'And': A Puzzle About Non-Conservative Extension. History and Philosophy of Logic 26 (3):229-266.
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