Article
| Title: | A Kalmár-style completeness proof for the logics of the hierarchy ${\mathbb{I}}^n {\mathbb{P}}^k$ (English) |
| Author: | Fernández, Víctor |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 485-509 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The logics of the family ${\mathbb{I}}^n {\mathbb{P}}^k$:=$\{{ I^n P^k}\}_{(n,k) \in \omega^2}$ are formally defined by means of finite matrices, as a simultaneous generalization of the weakly-intuitionistic logic $I^1$ and of the paraconsistent logic $P^1$. It is proved that this family can be naturally ordered, and it is shown a sound and complete axiomatics for each logic of the form $I^n P^k$. The involved completeness proof showed here is obtained by means of a generalization of the well-known Kalmár's method, usually applied for many-valued logics. (English) |
| Keyword: | mathematical logic |
| Keyword: | Kalmár's completeness proof |
| Keyword: | many-valued logic |
| MSC: | 03B50 |
| MSC: | 03B53 |
| DOI: | 10.14712/1213-7243.2024.009 |
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| Date available: | 2024-11-05T11:52:13Z |
| Last updated: | 2024-11-05 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152624 |
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