A linear logic framework for multimodal logics

نویسندگان

چکیده

Abstract One of the most fundamental properties a proof system is analyticity , expressing fact that given formula F only uses subformulas . In sequent calculus, this property usually proved by showing $\mathsf{cut}$ rule admissible, i.e., introduction auxiliary lemma H in reasoning “if follows from G and then ” can be eliminated. The cut admissibility tedious, error-prone process through several transformations, thus requiring assistance (semi-)automatic procedures. previous work Miller Pimentel, linear logic ( $\mathsf{LL}$ ) was used as logical framework for establishing sufficient conditions object systems (OL). OL’s inference rules are specified an theory easy-to-verify criterion sufficed to establish cut-admissibility theorem OL at hand. However, there many cannot adequately encoded symptomatic cases being modal logics. paper, we use linear-nested $\mathsf{LNS}$ presentation $\mathsf{MMLL}$ (a variant LL with subexponentials), show it possible (classical or substructural) multimodal We same approach suitable handling intuitionistic logic.

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ژورنال

عنوان ژورنال: Mathematical Structures in Computer Science

سال: 2022

ISSN: ['1469-8072', '0960-1295']

DOI: https://doi.org/10.1017/s0960129522000366