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- W2012346013 abstract "It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study how to reduce the weight of propositional deductions. We present the formalism of proof-graphs for purely implicational logic, which are graphs of a specific shape that are intended to capture the logical structure of a deduction. The advantage of this formalism is that formulas can be shared in the reduced proof. In the present paper we give a precise definition of proof-graphs for the minimal implicational logic, together with a normalization procedure for these proof-graphs. In contrast to standard tree-like formalisms, our normalization does not increase the number of nodes, when applied to the corresponding minimal proof-graph representations." @default.
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- W2012346013 date "2014-03-30" @default.
- W2012346013 modified "2023-09-28" @default.
- W2012346013 title "Proof-graphs for Minimal Implicational Logic" @default.
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- W2012346013 doi "https://doi.org/10.4204/eptcs.144.2" @default.
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