A note on strictly positive logics and word rewriting systems

Автор: Beklemishev Lev
Сборник: Larisa Maksimova on Implication, Interpolation, and Definability
Редактор: Одинцов Сергей Павлович
Серия: Outstanding Contributions to Logic
Том: 15
Глава в коллективной монографии
Год издания: 2018
Издательство: SPRINGER
Местоположение издательства: VAN GODEWIJCKSTRAAT 30, DORDRECHT, NETHERLANDS, 3311GZ
Первая страница: 61
Последняя страница: 70
DOI: 10.1007/978-3-319-69917-2_4
Аннотация: We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable finitely axiomatizable strictly positive normal modal logics. The translation has its counterpart on the level of proofs: we formulate a natural deep inference proof system for strictly positive logics generalizing derivations in word rewriting systems. We also make some observations and formulate open questions related to the theory of modal companions of superintuitionistic logics that was initiated by L.L. Maksimova and V.V. Rybakov.
Добавил в систему: Золин Евгений Евгеньевич

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