Genuine paracomplete logics
| Autor: | Verónica Borja Macías, Marcelo E Coniglio, Alejandro Hernández-Tello |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Logic Journal of the IGPL. |
| ISSN: | 1368-9894 1367-0751 |
| DOI: | 10.1093/jigpal/jzac060 |
| Popis: | In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws $\varphi ,\neg \varphi \vdash \psi $ and $\vdash \neg (\varphi \land \neg \varphi )$. In that paper, the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above-mentioned are $ \vdash \varphi , \neg \varphi $ and $\neg (\psi \vee \neg \psi ) \vdash $. We call genuine paracomplete logics those rejecting the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics. A very natural twist structures semantics for these logics is also found in a systematic way. This semantics produces automatically a simple and elegant Hilbert-style characterization for all these logics. Finally, we introduce the logic LGP which is genuine paracomplete is not genuine paraconsistent, not even paraconsistent and cannot be characterized by a single finite logical matrix. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|