Informal provability, first-order BAT logic and first steps towards a formal theory of informal provability
- Author
- Pawel Pawlowski (UGent) and Rafal Urbaniak (UGent)
- Organization
- Abstract
- BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to he extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not.
- Keywords
- MODAL SEMANTICS, REALIZABILITY, INDUCTION, informal provability, non-deterministic logic, BAT logic
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8759529
- MLA
- Pawlowski, Pawel, and Rafal Urbaniak. “Informal Provability, First-Order BAT Logic and First Steps towards a Formal Theory of Informal Provability.” LOGIC AND LOGICAL PHILOSOPHY, vol. 31, no. 3, 2022, pp. 501–27, doi:10.12775/LLP.2021.016.
- APA
- Pawlowski, P., & Urbaniak, R. (2022). Informal provability, first-order BAT logic and first steps towards a formal theory of informal provability. LOGIC AND LOGICAL PHILOSOPHY, 31(3), 501–527. https://doi.org/10.12775/LLP.2021.016
- Chicago author-date
- Pawlowski, Pawel, and Rafal Urbaniak. 2022. “Informal Provability, First-Order BAT Logic and First Steps towards a Formal Theory of Informal Provability.” LOGIC AND LOGICAL PHILOSOPHY 31 (3): 501–27. https://doi.org/10.12775/LLP.2021.016.
- Chicago author-date (all authors)
- Pawlowski, Pawel, and Rafal Urbaniak. 2022. “Informal Provability, First-Order BAT Logic and First Steps towards a Formal Theory of Informal Provability.” LOGIC AND LOGICAL PHILOSOPHY 31 (3): 501–527. doi:10.12775/LLP.2021.016.
- Vancouver
- 1.Pawlowski P, Urbaniak R. Informal provability, first-order BAT logic and first steps towards a formal theory of informal provability. LOGIC AND LOGICAL PHILOSOPHY. 2022;31(3):501–27.
- IEEE
- [1]P. Pawlowski and R. Urbaniak, “Informal provability, first-order BAT logic and first steps towards a formal theory of informal provability,” LOGIC AND LOGICAL PHILOSOPHY, vol. 31, no. 3, pp. 501–527, 2022.
@article{8759529,
abstract = {{BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to he extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not.}},
author = {{Pawlowski, Pawel and Urbaniak, Rafal}},
issn = {{1425-3305}},
journal = {{LOGIC AND LOGICAL PHILOSOPHY}},
keywords = {{MODAL SEMANTICS,REALIZABILITY,INDUCTION,informal provability,non-deterministic logic,BAT logic}},
language = {{eng}},
number = {{3}},
pages = {{501--527}},
title = {{Informal provability, first-order BAT logic and first steps towards a formal theory of informal provability}},
url = {{http://doi.org/10.12775/LLP.2021.016}},
volume = {{31}},
year = {{2022}},
}
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