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SMALL INFINITARY EPISTEMIC LOGICS
| Content Provider | Scilit |
|---|---|
| Author | Hu, Tai-Wei Kaneko, Mamoru Suzuki, Nobu-Yuki |
| Copyright Year | 2019 |
| Description | We develop a series of small infinitary epistemic logics to study deductive inference involving intra-/interpersonal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL $(L_{α}$) are presented for ordinal α up to a given _{α}$^{o}$ (_{α}$^{o}$ ≥ ω) so that $GL(L_{0}$) is finitary $KD^{n}$ with n agents and $GL(L_{α}$) (α ≥ 1) allows conjunctions of certain countably infinite formulae. $GL(L_{α}$) is small in that the language is countable and can be constructive. The set of formulae $L_{α}$ is increasing up to α = ω but stops at ω We present Kripke-completeness for $GL(L_{α}$) for each α ≤ ω, which is proved using the Rasiowa–Sikorski lemma and Tanaka–Ono lemma. $GL(L_{α}$) has a sufficient expressive power to discuss intra-/interpersonal beliefs with infinite lengths. As applications, we discuss the explicit definability of Axioms T (truthfulness), 4 (positive introspection), 5 (negative introspection), and of common knowledge in $GL(L_{α}$) Also, we discuss the rationalizability concept in game theory in our framework. We evaluate where these discussions are done in the series $GL(L_{α}$), α ≤ ω. |
| Related Links | https://research-information.bris.ac.uk/ws/files/182802146/GL2019Jan14.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1F6AE9378990B8EBC7C3D2320BAC705/S1755020319000029a.pdf/div-class-title-small-infinitary-epistemic-logics-div.pdf |
| Ending Page | 735 |
| Page Count | 34 |
| Starting Page | 702 |
| ISSN | 17550203 |
| e-ISSN | 17550211 |
| DOI | 10.1017/s1755020319000029 |
| Journal | The Review of Symbolic Logic |
| Issue Number | 4 |
| Volume Number | 12 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2019-12-01 |
| Access Restriction | Open |
| Subject Keyword | The Review of Symbolic Logic History and Philosophy of Science Infinitary Epistemic Logic Rasiowa–sikorski Lemma Explicit Definability Rationalizability |
| Content Type | Text |
| Resource Type | Article |
| Subject | Philosophy Logic |
