A classical-logic view on a paraconsistent logic
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909790606721024 |
|---|---|
| author | Middelburg, C. A. |
| author_facet | Middelburg, C. A. |
| contents | This paper is concerned with the paraconsistent first-order logic LPQ$^{\supset,\mathsf{F}}$, Priest's LPQ enriched with an implication connective and a falsity constant. A sequent-style natural deduction proof system for this logic is presented and, for this proof system, both a model-theoretic justification and a logical justification by means of an embedding into first-order classical logic is given. The given embedding provides in addition a classical-logic explanation of this paraconsistent logic. As a further matter, its use in decidability issues concerning this paraconsistent logic is discussed. The major properties of LPQ$^{\supset,\mathsf{F}}$ concerning its logical consequence relation and its logical equivalence relation are also treated. The paper emphasizes how closely LPQ$^{\supset,\mathsf{F}}$ is related to classical logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_07292 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A classical-logic view on a paraconsistent logic Middelburg, C. A. Logic in Computer Science Logic 03B53 (Primary) 03B10, 03B50, 03B25 (Secondary) This paper is concerned with the paraconsistent first-order logic LPQ$^{\supset,\mathsf{F}}$, Priest's LPQ enriched with an implication connective and a falsity constant. A sequent-style natural deduction proof system for this logic is presented and, for this proof system, both a model-theoretic justification and a logical justification by means of an embedding into first-order classical logic is given. The given embedding provides in addition a classical-logic explanation of this paraconsistent logic. As a further matter, its use in decidability issues concerning this paraconsistent logic is discussed. The major properties of LPQ$^{\supset,\mathsf{F}}$ concerning its logical consequence relation and its logical equivalence relation are also treated. The paper emphasizes how closely LPQ$^{\supset,\mathsf{F}}$ is related to classical logic. |
| title | A classical-logic view on a paraconsistent logic |
| topic | Logic in Computer Science Logic 03B53 (Primary) 03B10, 03B50, 03B25 (Secondary) |
| url | https://arxiv.org/abs/2008.07292 |