Abstract
We provide a complete axiomatization of modal inclusion logic—team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof system, and use the normal form to prove completeness of the axiomatization. Complete axiomatizations are also provided for two other extensions of modal logic with the same expressive power as modal inclusion logic: one augmented with a might operator and the other with a single-world variant of the might operator.
| Original language | English |
|---|---|
| Article number | 103102 |
| Journal | Archive for Mathematical Logic |
| DOIs | |
| Publication status | E-pub ahead of print - 27 Jan 2025 |
Bibliographical note
Publisher Copyright:© The Author(s) 2025.
Funding
This research was supported by Grant 336283 of Academy of Finland. Part of the first author\u2019s research was conducted while he was affiliated with the Department of Mathematics and Statistics, University of Helsinki, Finland, where he also received funding from the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programme (Grant Agreement No. 101020762). The second author was supported additionally by the Vilho, Yrj\u00F6 and Kalle V\u00E4is\u00E4l\u00E4 Foundation. The authors would like to thank the anonymous reviewer for their corrections as well as for their helpful suggestions concerning the presentation of the material in this article.
| Funders | Funder number |
|---|---|
| Research Council of Finland | |
| Vilho, Yrjö and Kalle Väisälä Foundation | |
| European Research Council | |
| Horizon 2020 Framework Programme | 101020762 |
Keywords
- Dependence logic
- Inclusion logic
- Modal logic
- Team semantics