About Logically Probable Sentences
The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value o...
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| Formato: | Artigo |
| Idioma: | English |
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Lodz University Press
2024-04-01
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| Series: | Bulletin of the Section of Logic |
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| Acceso en liña: | https://czasopisma.uni.lodz.pl/bulletin/article/view/20466 |
| _version_ | 1827097123050487808 |
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| author | Adam Olszewski |
| author_facet | Adam Olszewski |
| author_sort | Adam Olszewski |
| collection | DOAJ |
| description | The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered. |
| first_indexed | 2025-03-20T07:26:39Z |
| format | Article |
| id | doaj.art-addcdee4e48c46e6bb5a8302e3e58ef4 |
| institution | Directory Open Access Journal |
| issn | 0138-0680 2449-836X |
| language | English |
| last_indexed | 2025-03-20T07:26:39Z |
| publishDate | 2024-04-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Bulletin of the Section of Logic |
| spelling | doaj.art-addcdee4e48c46e6bb5a8302e3e58ef42024-09-30T13:29:33ZengLodz University PressBulletin of the Section of Logic0138-06802449-836X2024-04-0153336539710.18778/0138-0680.2024.0420308About Logically Probable SentencesAdam Olszewski0https://orcid.org/0000-0003-3069-7518Pontifical University of John Paul II in Cracow, Faculty of Philosophy The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered.https://czasopisma.uni.lodz.pl/bulletin/article/view/20466probable sentencesmajoritylogically probable formulaboolean valuation |
| spellingShingle | Adam Olszewski About Logically Probable Sentences Bulletin of the Section of Logic probable sentences majority logically probable formula boolean valuation |
| title | About Logically Probable Sentences |
| title_full | About Logically Probable Sentences |
| title_fullStr | About Logically Probable Sentences |
| title_full_unstemmed | About Logically Probable Sentences |
| title_short | About Logically Probable Sentences |
| title_sort | about logically probable sentences |
| topic | probable sentences majority logically probable formula boolean valuation |
| url | https://czasopisma.uni.lodz.pl/bulletin/article/view/20466 |
| work_keys_str_mv | AT adamolszewski aboutlogicallyprobablesentences |