Tableau Systems for Epistemic Positional Logics

Authors

  • Mateusz Klonowski Nicolaus Copernicus University, Department of Logic, ul. Stanisława Moniuszki 16/20, 87-100 Torun, Poland https://orcid.org/0000-0001-8616-9189
  • Krzysztof Aleksander Krawczyk Nicolaus Copernicus University, Department of Logic, ul. Stanisława Moniuszki 16/20, 87-100 Torun, Poland https://orcid.org/0000-0003-4367-4796
  • Bożena Pięta Nicolaus Copernicus University, Department of Logic, ul. Stanisława Moniuszki 16/20, 87-100 Torun, Poland https://orcid.org/0000-0002-6281-0469

DOI:

https://doi.org/10.18778/0138-0680.2021.06

Keywords:

epistemic logic, logical omniscience, positional logic, tableau system

Abstract

The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent ... knows/beliefs that ...’. The second one is to define tableau systems
for such logics. Firstly, we present the minimal positional logic MR. Then, we change the notion of formulas and semantics in order to consider iterations of the operator of realization and “free” classical formulas. After that, we move on to weaker logics in order to avoid the well known problem of logical omniscience. At the same time, we keep the positional counterparts of modal axioms (T), (4) and (5). For all of the considered logics we present sound and complete tableau systems.

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Published

2021-04-01

How to Cite

Klonowski, M., Krawczyk, K. A., & Pięta, B. (2021). Tableau Systems for Epistemic Positional Logics. Bulletin of the Section of Logic, 50(2), 177–204. https://doi.org/10.18778/0138-0680.2021.06

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Research Article