On the complexity of the disjunction property in intuitionistic and modal logics

Author:

Ferrari Mauro1,Fiorentini Camillo1,Fiorino Guido2

Affiliation:

1. Università degli Studi di Milano, Milan, Italy

2. Università degli Studi di Milano-Bicocca, Milan, Italy

Abstract

In this article we study the complexity of disjunction property for intuitionistic logic, the modal logics S4 , S4.1 , Grzegorczyk logic, Gödel-Löb logic, and the intuitionistic counterpart of the modal logic K . For S4 we even prove the feasible interpolation theorem and we provide a lower bound for the length of proofs. The techniques we use do not require proving structural properties of the calculi in hand, such as the cut-elimination theorem or the normalization theorem. This is a key point of our approach, since it allows us to treat logics for which only Hilbert-style characterizations are known.

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the proof complexity of logics of bounded branching;Annals of Pure and Applied Logic;2023-01

2. New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces;Journal of Function Spaces;2021-01-16

3. Proof Complexity of Non-classical Logics;Lecture Notes in Computer Science;2012

4. Proof Complexity of Non-classical Logics;Lecture Notes in Computer Science;2010

5. Substitution Frege and extended Frege proof systems in non-classical logics;Annals of Pure and Applied Logic;2009-05

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