Geodesic
A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models
Algebra i logika, Tome 44 (2005) no. 5, pp. 560-582.

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

An axiomatization is furnished for a polymodal logic of strictly linearly ordered $A$-frames: for frames of this kind, we consider a language of polymodal logic with two modal operators, $\Box_$ and $\Box_\prec$. In the language, along with the operators, we introduce a constant $\beta$, which describes a basis subset. In the language with the two modal operators and constant $\beta$, an $L\alpha$-calculus is constructed. It is proved that such is complete w. r. t the class of all strictly linearly ordered $A$-frames. Moreover, it turns out that the calculus in question possesses the finite-model property and, consequently, is decidable.
Mots-clés : calculus, polymodal logic
Keywords: strictly linearly ordered $A$-frame, decidability. 
@article{AL_2005_44_5_a2,
     author = {V. F. Murzina},
     title = {A {Modal} {Logic} {That} is {Complete} with {Respect} to {Strictly} {Linearly} {Ordered} $A${-Models}},
     journal = {Algebra i logika},
     pages = {560--582},
     publisher = {mathdoc},
     volume = {44},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2005_44_5_a2/}
}
TY  - JOUR
AU  - V. F. Murzina
TI  - A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models
JO  - Algebra i logika
PY  - 2005
SP  - 560
EP  - 582
VL  - 44
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2005_44_5_a2/
LA  - ru
ID  - AL_2005_44_5_a2
ER  - 
%0 Journal Article
%A V. F. Murzina
%T A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models
%J Algebra i logika
%D 2005
%P 560-582
%V 44
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2005_44_5_a2/
%G ru
%F AL_2005_44_5_a2
V. F. Murzina. A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models. Algebra i logika, Tome 44 (2005) no. 5, pp. 560-582. http://geodesic.mathdoc.fr/item/AL_2005_44_5_a2/

[1] Yu. L. Ershov, Theory of domains and nearby, Int. conf. formal methods programm. appl., Lec. Not. Comp. Sci., 735, Springer-Verlag, Novosibirsk, 1993 | MR

[2] V. F. Murzina, “Vremennye logiki, polnye otnositelnostrogo lineino uporyadochennykh $f$-modelei”, Vestnik NGU, 3:1 (2003), 61–82 | Zbl

[3] Yu. L. Ershov, “Teoriya $A$-prostranstv”, Algebra i logika, 12:4 (1973), 369–418 | MR

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