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

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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. 
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     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},
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     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2005_44_5_a2/}
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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/