Classical first-order logic:
One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surroundi...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2022
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| Series: | Cambridge elements
|
| Subjects: | |
| Links: | https://doi.org/10.1017/9781108982009 https://doi.org/10.1017/9781108982009 https://doi.org/10.1017/9781108982009 |
| Summary: | One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. We provide theorems about the system we developed, such as unique readability and the Lindenbaum lemma. We also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet |
| Item Description: | Title from publisher's bibliographic system (viewed on 07 Apr 2022) |
| Physical Description: | 1 Online-Ressource (71 Seiten) |
| ISBN: | 9781108982009 |
| DOI: | 10.1017/9781108982009 |
Staff View
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| isbn | 9781108982009 |
| language | English |
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| spelling | Shapiro, Stewart 1951- (DE-588)131540564 aut Classical first-order logic Stewart Shapiro, Teresa Kouri Kissel Cambridge Cambridge University Press 2022 1 Online-Ressource (71 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge elements Title from publisher's bibliographic system (viewed on 07 Apr 2022) One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. We provide theorems about the system we developed, such as unique readability and the Lindenbaum lemma. We also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet Logic, Symbolic and mathematical Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Stufe 1 (DE-588)4362503-4 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 s Stufe 1 (DE-588)4362503-4 s DE-604 Kouri Kissel, Teresa ca. 20./21. Jh. (DE-588)1260680320 aut Erscheint auch als Druck-Ausgabe 978-1-108-98700-4 https://doi.org/10.1017/9781108982009 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Shapiro, Stewart 1951- Kouri Kissel, Teresa ca. 20./21. Jh Classical first-order logic Logic, Symbolic and mathematical Prädikatenlogik (DE-588)4046974-8 gnd Stufe 1 (DE-588)4362503-4 gnd |
| subject_GND | (DE-588)4046974-8 (DE-588)4362503-4 |
| title | Classical first-order logic |
| title_auth | Classical first-order logic |
| title_exact_search | Classical first-order logic |
| title_full | Classical first-order logic Stewart Shapiro, Teresa Kouri Kissel |
| title_fullStr | Classical first-order logic Stewart Shapiro, Teresa Kouri Kissel |
| title_full_unstemmed | Classical first-order logic Stewart Shapiro, Teresa Kouri Kissel |
| title_short | Classical first-order logic |
| title_sort | classical first order logic |
| topic | Logic, Symbolic and mathematical Prädikatenlogik (DE-588)4046974-8 gnd Stufe 1 (DE-588)4362503-4 gnd |
| topic_facet | Logic, Symbolic and mathematical Prädikatenlogik Stufe 1 |
| url | https://doi.org/10.1017/9781108982009 |
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