Barwise's Information Frames and Modal Logics
Algebra i logika, Tome 41 (2002) no. 5, pp. 585-609.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article studies Barwise's information frames and settles the problem of Barwise dealing in finding 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; (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. Toward a general theory, we prove that any Kripke complete modal logic is a modal logic of a certain class of information frames, and that every modal logic generated by any given class of complete, rarefied, and fully classified information frames is Kripke complete.
Keywords: knowledge presentation, information flow, information frame, modal logic, Kripke model.
Mots-clés : information
@article{AL_2002_41_5_a4,
     author = {V. V. Rybakov},
     title = {Barwise's {Information} {Frames} and {Modal} {Logics}},
     journal = {Algebra i logika},
     pages = {585--609},
     publisher = {mathdoc},
     volume = {41},
     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_5_a4/}
}
TY  - JOUR
AU  - V. V. Rybakov
TI  - Barwise's Information Frames and Modal Logics
JO  - Algebra i logika
PY  - 2002
SP  - 585
EP  - 609
VL  - 41
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2002_41_5_a4/
LA  - ru
ID  - AL_2002_41_5_a4
ER  - 
%0 Journal Article
%A V. V. Rybakov
%T Barwise's Information Frames and Modal Logics
%J Algebra i logika
%D 2002
%P 585-609
%V 41
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_5_a4/
%G ru
%F AL_2002_41_5_a4
V. V. Rybakov. Barwise's Information Frames and Modal Logics. Algebra i logika, Tome 41 (2002) no. 5, pp. 585-609. http://geodesic.mathdoc.fr/item/AL_2002_41_5_a4/

[1] J. Barwise, “Information and impossibilities”, Notre Dame J. Formal Logic, 38:4 (1997), 488–515 | DOI | MR | Zbl

[2] F. Dretske, Knowledge and the Flow of Information, MIT Press, Bradford Books, 1981

[3] R. Stalnaker, “Impossibilities”, Philos. Topics, 24 (1996), 193–204

[4] C. Shannon, “The mathematical theory of communications”, Bell Syst. Tech. J., 27 (1948), 37–423, 623–656 | MR

[5] J. Barwise, J. Seligman, Information Flow in Distributed Systems, Tracts Theor. Comput. Sci., 44, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[6] J. Barwise, J. Perry, Situations and Attitudes, MIT Press, Bradford Books, 1983

[7] W. G. Lycan, Modality and Meaning, Kluwer Academic Publishers, 1994

[8] V. V. Rybakov, Admissibility of logical inference rules, Stud. Logic Found. Math., 136, Elsevier, Amsterdam–New York, 1997 | MR | Zbl

[9] A. Chagrov, M. Zakharyaschev, Modal logics, Oxford Logic Guides, 35, Clarendon Press, Oxford, 1997 | MR | Zbl

[10] S. Kripke, “Semantic Analysis of Modal Logic. II. Non-Normal Modal Propositional Calculi”, The Theory of Models, eds. J. W. Addison, L. Henkin, A. Tarski, North-Holland, Amsterdam, 1965, 206–220 | MR