The logical system MTL (for Monoidal t-norm Logic) is a formalism of the logic
of left-continuous t-norms, which are operations that arise in the study of fuzzy
sets and fuzzy logic. The objective is to investigate the important results on MTL
and collect them together in a coherent form. The main results considered will be
the completeness results for the logic with respect to MTL-algebras, MTL-chains
(linearly ordered MTL-algebras) and standard MTL-algebras (left-continuous t-norm
algebras). Completeness of MTL with respect to standard MTL-algebras means that
MTL is indeed the logic of left-continuous t-norms. The logical system BL (for Basic Logic) is an axiomatic extension of MTL; we will consider the same completeness results for BL; that is we will show that BL is complete with respect to BL-algebras, BL-chains and standard BL-algebras (continuous t-norm algebras). Completeness of BL with respect to standard BL-algebras means that BL is the logic of continuous t-norms.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/13694 |
| Date | 07 February 2014 |
| Creators | Toloane, Ellen Mohau |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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