The unification type of Lukasiewicz logic with a bounded number of variables
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915403777703936 |
|---|---|
| author | Abbadini, Marco Spada, Luca |
| author_facet | Abbadini, Marco Spada, Luca |
| contents | Building on the correspondence between finitely axiomatised theories in Łukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of Łukasiewicz logic with $n\geq 2$ variables is nullary. This solves a problem left open in [V. Marra and L. Spada. Ann. Pure Appl. Logic 164 2013, p. 192-210]. Furthermore, we refine the study of unification with bounds on the number of variables. Our proposal distinguishes the number $m$ of variables allowed in the problem and the number $n$ in the solution. We prove that the unification type of Łukasiewicz logic for all $m,n \geq 2$ is nullary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The unification type of Lukasiewicz logic with a bounded number of variables Abbadini, Marco Spada, Luca Logic Primary: 06D35. Secondary: 03C05, 52B20, 57M10 Building on the correspondence between finitely axiomatised theories in Łukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of Łukasiewicz logic with $n\geq 2$ variables is nullary. This solves a problem left open in [V. Marra and L. Spada. Ann. Pure Appl. Logic 164 2013, p. 192-210]. Furthermore, we refine the study of unification with bounds on the number of variables. Our proposal distinguishes the number $m$ of variables allowed in the problem and the number $n$ in the solution. We prove that the unification type of Łukasiewicz logic for all $m,n \geq 2$ is nullary. |
| title | The unification type of Lukasiewicz logic with a bounded number of variables |
| topic | Logic Primary: 06D35. Secondary: 03C05, 52B20, 57M10 |
| url | https://arxiv.org/abs/2504.19011 |