Geodesic
Axiomatization and Polynomial Solvability of Strictly Positive Fragments of Certain Modal Logics
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 884-901

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The fragment of the language of modal logic that consists of all implications $A\to B$, where $A$ and $B$ are built from variables, the constant $\top$ (truth), and the connectives $\wedge$ and $\diamondsuit_1, \diamondsuit_2, \dots, \diamondsuit_m$. For the polymodal logic $S5_m$ (the logic of $m$ equivalence relations) and the logic $K4.3$ (the logic of irreflexive linear orders), an axiomatization of such fragments is found and their algorithmic decidability in polynomial time is proved.
Keywords: strictly positive modal logic, epistemic logic. 
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     author = {M. V. Svyatlovskiy},
     title = {Axiomatization and {Polynomial} {Solvability} of {Strictly} {Positive} {Fragments} of {Certain} {Modal} {Logics}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a7/}
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M. V. Svyatlovskiy. Axiomatization and Polynomial Solvability of Strictly Positive Fragments of Certain Modal Logics. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 884-901. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a7/