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- W3036658788 abstract "In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $mathbf{P}$ at least as strong as Full Lambek calculus, $mathbf{FL}$, and polynomially simulated by the extended Frege system for some infinite branching super-intuitionistic logic, we present an exponential lower bound on the proof lengths. More precisely, we will provide a sequence of $mathbf{P}$-provable formulas ${A_n}_{n=1}^{infty}$ such that the length of the shortest $mathbf{P}$-proof for $A_n$ is exponential in the length of $A_n$. The lower bound also extends to the number of proof-lines (proof-lengths) in any Frege system (extended Frege system) for a logic between $mathsf{FL}$ and any infinite branching super-intuitionistic logic. We will also prove a similar result for the proof systems and logics extending Visser's basic propositional calculus $mathbf{BPC}$ and its logic $mathsf{BPC}$, respectively. Finally, in the classical substructural setting, we will establish an exponential lower bound on the number of proof-lines in any proof system polynomially simulated by the cut-free version of $mathbf{CFL_{ew}}$." @default.
- W3036658788 created "2020-06-25" @default.
- W3036658788 creator A5007377083 @default.
- W3036658788 date "2020-06-17" @default.
- W3036658788 modified "2023-10-18" @default.
- W3036658788 title "Proof Complexity of Substructural Logics" @default.
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