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Towards a Combinatorial Proof Theory

Benjamin Ralph 1 Lutz Straßburger 1, 2
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : The main part of a classical combinatorial proof is a skew fi-bration, which precisely captures the behavior of weakening and contraction. Relaxing the presence of these two rules leads to certain substruc-tural logics and substructural proof theory. In this paper we investigate what happens if we replace the skew fibration by other kinds of graph homomorphism. This leads us to new logics and proof systems that we call combinatorial.
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Submitted on : Tuesday, December 3, 2019 - 9:44:20 AM
Last modification on : Friday, April 30, 2021 - 10:02:41 AM
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Benjamin Ralph, Lutz Straßburger. Towards a Combinatorial Proof Theory. TABLEAUX 2019 - 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Sep 2019, London, United Kingdom. pp.259-276, ⟨10.1007/978-3-030-29026-9_15⟩. ⟨hal-02390417⟩

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