The Modal Cube Revisited: Semantics without Worlds (Technical Report)
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911055380217856 |
|---|---|
| author | Leme, Renato Olarte, Carlos Pimentel, Elaine Coniglio, Marcelo E. |
| author_facet | Leme, Renato Olarte, Carlos Pimentel, Elaine Coniglio, Marcelo E. |
| contents | We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each logic, where necessitation is captured by the systematic use of level valuations. The semantics is grounded in an eight-valued system and provides a sound and complete decision procedure for each modal logic, extending and refining earlier semantics as particular cases. Additionally, we propose a novel model-theoretic perspective that links our framework to relational (Kripke-style) semantics, addressing longstanding conjectures regarding the correspondence between modal axioms and semantic conditions within non-deterministic settings. The result is a philosophically robust and technically modular alternative to standard possible-world semantics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Modal Cube Revisited: Semantics without Worlds (Technical Report) Leme, Renato Olarte, Carlos Pimentel, Elaine Coniglio, Marcelo E. Logic in Computer Science We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each logic, where necessitation is captured by the systematic use of level valuations. The semantics is grounded in an eight-valued system and provides a sound and complete decision procedure for each modal logic, extending and refining earlier semantics as particular cases. Additionally, we propose a novel model-theoretic perspective that links our framework to relational (Kripke-style) semantics, addressing longstanding conjectures regarding the correspondence between modal axioms and semantic conditions within non-deterministic settings. The result is a philosophically robust and technically modular alternative to standard possible-world semantics. |
| title | The Modal Cube Revisited: Semantics without Worlds (Technical Report) |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2505.12824 |