Abstract
Surely we may say that the logic of propositional attitudes has established its position. It has been systematically studied for more than thirty years now (and of course it had already medieval ancestors). It has been equipped with highly sophisticated formal techniques. And it is no longer simply logic of knowledge and belief, but also other attitudes have been discussed in the same framework — at least perception, memory and imagination, as well as different varieties of doxastic commitment. Moreover, attitude logic, which was first somewhat controversial, has become a respectable tool in philosophical practice, so that it is freely used for various applications.
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Notes
See R. Bull and K. Segerberg, “Basic modal logic”, in Gabbay and Guenthner (eds.), Handbook of Philosophical Logic, Vol. II, Dordrecht 1984, and J. van Benthem, Modal Logic and Classical Logic, Napoli 1985.
The original papers are J.C.C. McKinsey and A. Tarski, “The algebra of topology”, Annals of Mathematics 45 (1944), and “On closed elements in closure algebras”, ibid. 47 (1946), B. Jónsson and A. Tarski, “Boolean algebras with operators”, American Journal of Mathematics 73 and 74 (1951–52).
As classics of metamathematical logic, see e.g. H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, Warsaw 1963, H. Rasiowa, “Algebraic treatment of the functional calculi of Heyting and Lewis”, Fundamenta mathematicae 38 (1951). Also the tradition of universal algebra is important here. On algebraic modal logic, cf. R.I. Goldblatt, “Metamathematics of modal logic”, Reports of Mathematical Logic 6 and 7 (1976), W.J. Blok, “The lattice of modal logics”, Journal of Symbolic Logic 45 (1980), and the review by R. Bull in JSL 48 (1983).
W. Rautenberg, “Der Verband der normalen verzweigten Modallogiken”, Mathematische Zeitschrift 156 (1977), M. Kracht and F. Wolter, “Properties of independently axiomatizable bimodal logics”, JSL 56 (1991). Kracht and Wolter observe rightly: “Monomodal logic is… a well-understood subject in contrast to polymodal logic, where even the most elementary questions concerning completeness, decidability, etc. have been left unanswered. Given that in many applications of modal logic one modality is not sufficient, the lack of general results is acutely felt by the “users” of modal logics.”
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© 1994 Springer Science+Business Media Dordrecht
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Aho, T. (1994). On the Interpretation of Attitude Logics. In: Prawitz, D., Westerståhl, D. (eds) Logic and Philosophy of Science in Uppsala. Synthese Library, vol 236. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8311-4_1
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DOI: https://doi.org/10.1007/978-94-015-8311-4_1
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