Affiliation:
1. Vienna University of Technology
Abstract
What can (and cannot) be expressed by structural display rules? Given a display calculus, we present a systematic procedure for transforming axioms into structural rules. The conditions for the procedure are given in terms of (purely syntactic) abstract properties of the base calculus; thus, the method applies to large classes of calculi and logics. If the calculus satisfies certain additional properties, we prove the converse direction, thus characterising the class of axioms that can be captured by structural display rules. Determining if an axiom belongs to this class or not is shown to be decidable. Applied to the display calculus for tense logic, we obtain a new proof of Kracht’s Display Theorem I.
Funder
Austrian Science Fund (FWF), START
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
17 articles.
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1. Algebraic Proof Theory for LE-logics;ACM Transactions on Computational Logic;2024-01-17
2. Multi-type Calculi and Structural Control;Electronic Proceedings in Theoretical Computer Science;2023-08-07
3. Linear Logic Properly Displayed;ACM Transactions on Computational Logic;2023-01-28
4. Syntactic Completeness of Proper Display Calculi;ACM Transactions on Computational Logic;2022-10-20
5. Display to Labeled Proofs and Back Again for Tense Logics;ACM Transactions on Computational Logic;2021-06-24