Geodesic
Theories in propositional logiс and the converse of substitution
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 33-41

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The paper considers the question of the existence and number of substitutional logics. It is proved that every tabular logic with a functionally complete system of connectives is substitutional. For these logics, the existence of an algorithm is proved, which, for a recursive consistent axiomatic of the theory, constructs an exact unifying substitution for it. A countable set of substitutional tabular logics is constructed. Some substitutional tabular logics with meaningful interpretation are presented. In addition, it is proved that every substitutional logic has a characteristic matrix. It is proved that there are continuum of nonsubstitutional logics.
Keywords: substitutional tabular logic, superintuitionistic logic, Lukasiewicz's logic. 
@article{IVM_2022_5_a2,
     author = {I. A. Gorbunov},
     title = {Theories in propositional logi{\cyrs} and the converse of substitution},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--41},
     publisher = {mathdoc},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_5_a2/}
}
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I. A. Gorbunov. Theories in propositional logiс and the converse of substitution. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 33-41. http://geodesic.mathdoc.fr/item/IVM_2022_5_a2/