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Saul Kripke (1963)
Semantical Analysis of Modal Logic I Normal Modal Propositional CalculiMathematical Logic Quarterly, 9
W. Alston, Fred Dretske (1985)
Knowledge and the Flow of Information
C. Shannon (1948)
A mathematical theory of communicationBell Syst. Tech. J., 27
W. Lycan (1994)
Modality and meaning
Jon Barwise (1997)
Information and ImpossibilitiesNotre Dame J. Formal Log., 38
N. Cocchiarella, J. Barwise, J. Perry (1986)
Situations and Attitudes.Journal of Symbolic Logic, 51
A. Chagrov, M. Zakharyaschev (1997)
Modal Logic (Oxford Logic Guides, vol. 35)
The paper studies Barwise's information frames and answers the John Barwise question: to find axiomatizations for the modal logics generated by information frames. We find axiomatic systems for (i) the modal logic of all complete information frames, (ii) the logic of all sound and complete information frames, (iii) the logic of all hereditary and complete information frames, (iv) the logic of all complete, sound and hereditary information frames, and (v) the logic of all consistent and complete information frames. The notion of weak modal logics is also proposed, and it is shown that the weak modal logics generated by all information frames and by all hereditary information frames are K and K4 respectively. To develop general theory, we prove that (i) any Kripke complete modal logic is the modal logic of a certain class of information frames and that (ii) the modal logic generated by any given class of complete, rarefied and fully classified information frames is Kripke complete. This paper is dedicated to the memory of talented mathematician John Barwise.
Archive for Mathematical Logic – Springer Journals
Published: Apr 1, 2003
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