We define a fragment of propositional logic where isomorphic propositions, such as A wedge B and B wedge A, or A ==> (B wedge C) and (A ==> B) wedge (A ==> C) are identified. We define System I, a proof language for this logic, and prove its normalisation and consistency.
@InProceedings{diazcaro_et_al:LIPIcs.FSCD.2019.14, author = {D{\'\i}az-Caro, Alejandro and Dowek, Gilles}, title = {{Proof Normalisation in a Logic Identifying Isomorphic Propositions}}, booktitle = {4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)}, pages = {14:1--14:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-107-8}, ISSN = {1868-8969}, year = {2019}, volume = {131}, editor = {Geuvers, Herman}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.14}, URN = {urn:nbn:de:0030-drops-105210}, doi = {10.4230/LIPIcs.FSCD.2019.14}, annote = {Keywords: Simply typed lambda calculus, Isomorphisms, Logic, Cut-elimination, Proof-reduction} }
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