Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 3 min ago
PreprintCC BY 4.0arXiv

Closure Semantics for Weak Modal Logics: Completeness and Representations

  • Yuki Nishimura
Open at sourcePDFDOICite

Abstract

Weak modal logics can be obtained by restricting the axioms and inference rules governing the modal operator. At the extreme, one may consider the least modal logic, in which no specifically modal axiom or inference rule is imposed. We introduce closure semantics, a new possible-world semantics for such weak modal logics, and establish soundness and strong completeness for a range of systems. We also give truth-preserving translations between closure models and other possible-world semantics, including neighborhood, FMT, and Kripke semantics.

Related

  1. Frobenius Galois expansions of substructural logics:Algebraization, Kalman equivalence and positive cone semantics
    Juntao Wang, jieqiong Shi, Mei Wang
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv
  2. Uncountably many maximally consistent neighborhood complete congruential modal logics
    Zalán Gyenis, Krzysztof Krawczyk
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv
  3. Intuitionistic and Constructive Modal Logics for Classical Modal Logicians
    Yuta Sato
    arXivPreprintarXiv licenceFull textLogic & foundationsarXiv
  4. Elementary modal logics and circuit complexity
    Tenyo Takahashi
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv
  5. Classical and Quantum Logics with Multiple Non-Equivalent and Non-Isomorphic Models
    Mladen Pavicic
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryLogic & foundationsarXiv

Cite

BibTeXRIS
BibTeX
@misc{nishimura2026closure,
  title = {{Closure Semantics for Weak Modal Logics: Completeness and Representations}},
  author = {Yuki Nishimura},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01433},
  eprint = {2610.01433},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01433},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Closure Semantics for Weak Modal Logics: Completeness and Representations
AU  - Yuki Nishimura
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.01433
UR  - https://arxiv.org/abs/2610.01433
AB  - Weak modal logics can be obtained by restricting the axioms and inference rules governing the modal operator. At the extreme, one may consider the least modal logic, in which no specifically modal axiom or inference rule is imposed. We introduce closure semantics, a new possible-world semantics for such weak modal logics, and establish soundness and strong completeness for a range of systems. We also give truth-preserving translations between closure models and other possible-world semantics, including neighborhood, FMT, and Kripke semantics.
ER  -