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 Algebra Logika: Year: Volume: Issue: Page: Find

 Algebra Logika, 2005, Volume 44, Number 5, Pages 560–582 (Mi al131)

A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models

V. F. Murzina

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: 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.

Keywords: calculus, polymodal logic, strictly linearly ordered $A$-frame, decidability

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English version:
Algebra and Logic, 2005, 44:5, 313–325

Bibliographic databases:

UDC: 512.543.7

Citation: V. F. Murzina, “A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models”, Algebra Logika, 44:5 (2005), 560–582; Algebra and Logic, 44:5 (2005), 313–325

Citation in format AMSBIB
\Bibitem{Mur05} \by V.~F.~Murzina \paper A Modal Logic That is Complete with Respect to Strictly Linearly Ordered $A$-Models \jour Algebra Logika \yr 2005 \vol 44 \issue 5 \pages 560--582 \mathnet{http://mi.mathnet.ru/al131} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2195020} \zmath{https://zbmath.org/?q=an:1106.03015} \transl \jour Algebra and Logic \yr 2005 \vol 44 \issue 5 \pages 313--325 \crossref{https://doi.org/10.1007/s10469-005-0030-z} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-27544473747} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. F. Murzina, “Freedom from the interpolation property for tense calculi associated with Ershov spaces”, Algebra and Logic, 46:6 (2007), 409–418
2. V. F. Murzina, “Temporal logic of linearly ordered $\alpha$-spaces”, Algebra and Logic, 47:6 (2008), 405–419
3. V. F. Murzina, “Absence of the interpolation property in the calculi $L\alpha$ and $Lf$”, Siberian Math. J., 49:1 (2008), 147–151
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