caa a22 4500 465779514 CHVBK 20180323111951.0 cr unu---uuuuu 170327e19900601xx s 000 0 eng 10.1007/BF00935599 doi (NATIONALLICENCE)springer-10.1007/BF00935599 Humberstone I. Department of Philosophy, Monash University, 3168, Clayton, Victoria, Australia aut Expressive power and semantic completeness: Boolean connectives in modal logic [Elektronische Daten] [I. Humberstone] 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). Polish Academy of Sciences, 1990 Studia Logica Kluwer Academic Publishers 49/2(1990-06-01), 197-214 0039-3215 49:2<197 1990 49 11225 https://doi.org/10.1007/BF00935599 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00935599 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Humberstone I. Department of Philosophy, Monash University, 3168, Clayton, Victoria, Australia aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/2(1990-06-01), 197-214 0039-3215 49:2<197 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer