Modular many-valued semantics for combined logics
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916252766699520 |
|---|---|
| author | Caleiro, Carlos Marcelino, Sérgio |
| author_facet | Caleiro, Carlos Marcelino, Sérgio |
| contents | We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics of strengthening a given many-valued logic with additional axioms, the study of conditions under which a given logic may be seen as a combination of simpler syntactically defined fragments whose calculi can be obtained independently and put together to form a calculus for the whole logic, and also general conditions for decidability to be preserved by the combination mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02189 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Modular many-valued semantics for combined logics Caleiro, Carlos Marcelino, Sérgio Logic Logic in Computer Science 03B62, 03B50 We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics of strengthening a given many-valued logic with additional axioms, the study of conditions under which a given logic may be seen as a combination of simpler syntactically defined fragments whose calculi can be obtained independently and put together to form a calculus for the whole logic, and also general conditions for decidability to be preserved by the combination mechanism. |
| title | Modular many-valued semantics for combined logics |
| topic | Logic Logic in Computer Science 03B62, 03B50 |
| url | https://arxiv.org/abs/2202.02189 |