Geodesic
On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$
Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 331-346

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The fragment of the polymodal provability logic $\mathbf{GLP}$ in the language with connectives $\top$, $\wedge$, and $\langle n\rangle$ for all $n\in\omega$ is considered. For this fragment, a deductive system it constructed, a Kripke semantics is proposed, and a polynomial bound for the complexity of a decision procedure is obtained.
Keywords: modal logic, graded provability logic $\mathbf{GLP}$, deductive system, Kripke semantics, complexity of a decision procedure.
Mots-clés : equational calculus 
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     author = {E. V. Dashkov},
     title = {On the {Positive} {Fragment} of the {Polymodal} {Provability} {Logic} $\mathbf{GLP}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {331--346},
     publisher = {mathdoc},
     volume = {91},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a1/}
}
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E. V. Dashkov. On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$. Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 331-346. http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a1/