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Mat. Zametki, 2002, Volume 72, Issue 6, Pages 853–868 (Mi mz472)  

This article is cited in 2 scientific papers (total in 2 papers)

Sequential Reflexive Logics with Noncontingency Operator

E. E. Zolin

M. V. Lomonosov Moscow State University

Abstract: Hilbert systems $L^\vartriangleright$ and sequential calculi $[L^\vartriangleright]$ for the versions of logics $L=\mathbf T,\mathbf {S4},\mathbf B,\mathbf {S5}$, and $\mathbf {Grz}$ stated in a language with the single modal noncontingency operator $\vartriangleright A=\square A\vee \square \neg A$ are constructed. It is proved that cut is not eliminable in the calculi $[L^\vartriangleright]$, but we can restrict ourselves to analytic cut preserving the subformula property. Thus the calculi $[\mathbf T^\vartriangleright]$, $[\mathbf {S4}^\vartriangleright]$, $[\mathbf {S5}^\vartriangleright ]$ ($[\mathbf {Grz}^\vartriangleright]$, respectively) satisfy the (weak, respectively) subformula property; for $[\mathbf B_2^\vartriangleright]$, this question remains open. For the noncontingency logics in question, the Craig interpolation property is established.

DOI: https://doi.org/10.4213/mzm472

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English version:
Mathematical Notes, 2002, 72:6, 784–798

Bibliographic databases:

UDC: 510.653
Received: 26.10.2000

Citation: E. E. Zolin, “Sequential Reflexive Logics with Noncontingency Operator”, Mat. Zametki, 72:6 (2002), 853–868; Math. Notes, 72:6 (2002), 784–798

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pan T., Yang Ch., “A Logic For Weak Essence and Strong Accident”, Log. Anal., 2017, no. 238, 179–190  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Chen J., Pan T., “Logic For Describing Strong Belief-Disagreement Between Agents”, Stud. Log., 106:1 (2018), 35–47  crossref  mathscinet  zmath  isi  scopus  scopus
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