Kulacka, Agnieszka (2018) Strong standard completeness for continuous t-norms. Fuzzy Sets and Systems 345 , pp. 139-150. ISSN 0165-0114.
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Abstract
This paper presents a proof of a strong completeness theorem for an extended axiomatic system of fuzzy logic BL with respect to all continuous t-norms. A finite strong standard completeness theorem for all continuous t-norms and their residua, the basic fuzzy logic, was proved across two papers Hájek (1998) and Cignoli et al. (2000). In Montagna (2007), the language of BL is extended by an additional connective and the axiomatic system includes an infinitary rule to achieve strong completeness result. In this paper we provide a proof of strong completeness for BL with a different infinitary inference rule but without extending the language of BL. We will also prove strong completeness for the Łukasiewicz and product t-norms using this extended axiomatic system.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Agnieszka Kulacka |
| Date Deposited: | 04 Feb 2025 11:04 |
| Last Modified: | 06 Apr 2025 14:57 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/54791 |
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