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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Lodz University Press
2024-11-01
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| Series: | Bulletin of the Section of Logic |
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| Online Access: | https://czasopisma.uni.lodz.pl/bulletin/article/view/22207 |
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| author | Marcin Czakon |
| author_facet | Marcin Czakon |
| author_sort | Marcin Czakon |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-252fca1d369244ae9351d43c0e392851 |
| institution | Kabale University |
| issn | 0138-0680 2449-836X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Bulletin of the Section of Logic |
| spelling | doaj-art-252fca1d369244ae9351d43c0e3928512025-02-07T07:22:47ZengLodz University PressBulletin of the Section of Logic0138-06802449-836X2024-11-0153447948910.18778/0138-0680.2024.1522374D-complete Single Axioms for the Equivalential Calculus with the rules D and RMarcin Czakon0https://orcid.org/0000-0001-6217-6640John Paul II Catholic University of Lublin, Department of Logic, Poland 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.https://czasopisma.uni.lodz.pl/bulletin/article/view/22207equivalential calculusd-completesingle axiomcondensed detachment |
| spellingShingle | Marcin Czakon D-complete Single Axioms for the Equivalential Calculus with the rules D and R Bulletin of the Section of Logic equivalential calculus d-complete single axiom condensed detachment |
| title | D-complete Single Axioms for the Equivalential Calculus with the rules D and R |
| title_full | D-complete Single Axioms for the Equivalential Calculus with the rules D and R |
| title_fullStr | D-complete Single Axioms for the Equivalential Calculus with the rules D and R |
| title_full_unstemmed | D-complete Single Axioms for the Equivalential Calculus with the rules D and R |
| title_short | D-complete Single Axioms for the Equivalential Calculus with the rules D and R |
| title_sort | d complete single axioms for the equivalential calculus with the rules d and r |
| topic | equivalential calculus d-complete single axiom condensed detachment |
| url | https://czasopisma.uni.lodz.pl/bulletin/article/view/22207 |
| work_keys_str_mv | AT marcinczakon dcompletesingleaxiomsfortheequivalentialcalculuswiththerulesdandr |