D-complete Single Axioms for the Equivalential Calculus with the rules D and R
Ulrich showed that most of the known axiomatisations of the classical equivalence calculus (EC) are D-incomplete, that is, they are not complete with the condensed detachment rule (D) as the primary rule of the proof procedure. He proved that the axiomatisation EEpEqrErEqp, EEEpppp by Wajsberg is D-...
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| Format: | Article |
| Language: | English |
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Lodz University Press
2024-11-01
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| Series: | Bulletin of the Section of Logic |
| Subjects: | |
| Online Access: | https://czasopisma.uni.lodz.pl/bulletin/article/view/22207 |
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| Summary: | Ulrich showed that most of the known axiomatisations of the classical equivalence calculus (EC) are D-incomplete, that is, they are not complete with the condensed detachment rule (D) as the primary rule of the proof procedure. He proved that the axiomatisation EEpEqrErEqp, EEEpppp by Wajsberg is D-complete and pointed out a number of D-complete single axioms, including one organic single axiom. In this paper we present new single axioms for EC with the condensed detachment and the reversed condensed detachment rules that form D-complete bases and are organic. |
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| ISSN: | 0138-0680 2449-836X |