L773:1611 3349 OR L773:0302 9743
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Abstract Cyclic Proofs (Extended abstract)
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- Afshari, Bahareh, 1981 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för filosofi, lingvistik och vetenskapsteori,Department of Philosophy, Linguistics and Theory of Science
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- Wehr, Dominik, 1998 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för filosofi, lingvistik och vetenskapsteori,Department of Philosophy, Linguistics and Theory of Science
- (creator_code:org_t)
- 2022-09-09
- 2022
- English.
- In: Lecture Notes in Computer Science, 28th International Workshop on Logic, Language, Information and Computation, Iași, Romania, September 20–23, 2022, Proceedings. - Cham : Springer. - 0302-9743 .- 1611-3349. - 9783031152979
- Conference paper (peer-reviewed)
Abstract
Subject headings
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- Cyclic proof systems permit derivations that are finite graphs in contrast to conventional derivation trees. The soundness of such proofs is ensured by a condition on the paths through the derivation graph, known as the global trace condition. To give a uniform treatment of such cyclic proof systems, Brotherston proposed an abstract notion of trace. We extend Brotherston’s approach into a category theoretical rendition of cyclic derivations, advancing the framework in two ways: First, we introduce activation algebras which allow for a more natural formalisation of trace conditions in extant cyclic proof systems. Second, accounting for the composition of trace information allows us to derive novel results about cyclic proofs, such as introducing the Ramsey trace condition.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Keyword
- Category Theory
- Cyclic Proof Theory
- Mu-Calculus
Publication and Content Type
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- kon (subject category)
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