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http://hdl.handle.net/11320/5562
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Pole DC | Wartość | Język |
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dc.contributor.author | Giero, Mariusz | - |
dc.date.accessioned | 2017-06-02T11:55:30Z | - |
dc.date.available | 2017-06-02T11:55:30Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Formalized Mathematics, Volume 24, Issue 4, pp. 281-290 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/5562 | - |
dc.description.abstract | This article introduces propositional logic as a formal system ([14], [10], [11]). The formulae of the language are as follows φ ::= ⊥ | p | φ → φ. Other connectives are introduced as abbrevations. The notions of model and satisfaction in model are defined. The axioms are all the formulae of the following schemes α ⇒ (β ⇒ α),(α ⇒ (β ⇒ γ)) ⇒ ((α ⇒ β) ⇒ (α ⇒ γ)),(¬β ⇒ ¬α) ⇒ ((¬β ⇒ α) ⇒ β). Modus ponens is the only derivation rule. The soundness theorem and the strong completeness theorem are proved. The proof of the completeness theorem is carried out by a counter-model existence method. In order to prove the completeness theorem, Lindenbaum’s Lemma is proved. Some most widely used tautologies are presented. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.subject | completeness | - |
dc.subject | formal system | - |
dc.subject | Lindenbaum’s lemma | - |
dc.title | The Axiomatization of Propositional Logic | - |
dc.type | Article | - |
dc.identifier.doi | 10.1515/forma-2016-0024 | - |
dc.description.Affiliation | Faculty of Economics and Informatics, University of Białystok, Kalvariju 135, LT-08221 Vilnius, Lithuania | - |
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Występuje w kolekcji(ach): | Artykuły naukowe (WEI) Formalized Mathematics, 2016, Volume 24, Issue 4 |
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forma-2016-0024.pdf | 273,29 kB | Adobe PDF | Otwórz |
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