Non-Strictly Positive Fixed-Points for Classical Natural Deduction, accepted for publication in APAL (2004)
| Citations: | 3 - 0 self |
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@TECHREPORT{Matthes04non-strictlypositive,
author = {Ralph Matthes},
title = {Non-Strictly Positive Fixed-Points for Classical Natural Deduction, accepted for publication in APAL},
institution = {},
year = {2004}
}
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Abstract
Termination for classical natural deduction is difficult in the presence of commuting/permutative conversions for disjunction. An approach based on reducibility candidates is presented that uses non-strictly positive inductive definitions. It covers second-order universal quantification and also the extension of the logic by fixed-points of non-strictly positive operators, which appears to be a new result. Finally, the relation to Parigot’s strictly-positive inductive definition of his set of reducibility candidates and to his notion of generalized reducibility candidates is explained. Key words: PACS:
