A logical characterization of multi-adjoint algebras
| Autor: | Jesús Medina, Luis Fariñas del Cerro, M. Eugenia Cornejo |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Soundness
0209 industrial biotechnology Logic Algebraic structure Axiomatic system 02 engineering and technology Logical connective Algebra 020901 industrial engineering & automation Artificial Intelligence Simple (abstract algebra) Computer Science::Logic in Computer Science Completeness (logic) Bounded function 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Axiom Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 425:140-156 |
| ISSN: | 0165-0114 |
| Popis: | This paper introduces a logical characterization of multi-adjoint algebras with a twofold contribution. On the one hand, the study of multi-adjoint algebras, from a logical perspective, will allow us to discover both the core and new features of these algebras. On the other hand, the axiomatization of multi-adjoint algebras will be useful to take advantage of the properties of the logical connectives considered in the corresponding deductive system. The mechanism considered to carry out the mentioned axiomatization follows the one given by Petr Hajek for residuated lattices. Specifically, the paper presents the bounded poset logic (BPL) as an axiomatization of a bounded poset, since this algebraic structure is the most simple structure from which a multi-adjoint algebra is defined. In the following, the language of BPL is enriched with a family of pairs, composed of a conjunctor and an implication, and its axiomatic system is endowed with new axioms, giving rise to the multi-adjoint logic (ML). The soundness and completeness of BPL and ML are proven. Finally, a comparison between the axiomatization of the multi-adjoint logic and the one given for the BL logic is introduced. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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