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This article is cited in 4 scientific papers (total in 4 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.
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
Linking options:
https://www.mathnet.ru/eng/mzm472https://doi.org/10.4213/mzm472 https://www.mathnet.ru/eng/mzm/v72/i6/p853
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