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Formulas of first-order logic in distributive normal form
Bibliography: leaves 140-143.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867614327892082688 |
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| access_status_str | Open Access |
| author | Nelte, Karen |
| author2 | Brink, Chris |
| author_browse | Brink, Chris Nelte, Karen |
| author_facet | Brink, Chris Nelte, Karen |
| author_sort | Nelte, Karen |
| collection | Thesis |
| description | Bibliography: leaves 140-143. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/9648 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:50:17.463Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/9648 Formulas of first-order logic in distributive normal form Nelte, Karen Brink, Chris Kieseppä, Ilkka Mathematics Bibliography: leaves 140-143. It was shown by Jaakko Hintikka that every formula of first-order logic can be written as a disjunction of formulas called constituents. Such a disjunction is called a distributive normal form of the formula. It is a generalization of the disjunctive normal form for propositional logic. However, there are some significant differences between these two normal forms, caused chiefly by the impossibility of defining the constituents in such a way that they are all consistent. Distributive normal forms and some of their properties are studied. For example, the size of distributive normal forms is examined, and although we can't determine exactly how many constituents (of each form) are consistent, it is shown that the vast majority are inconsistent. Hintikka's definition of trivial inconsistency is studied, and a new definition of trivial inconsistency is given in terms of a necessary condition for the consistency of a constituent which is stronger than the condition which Hintikka used in his definition of trivial inconsistency. An error in Hintikka's attempted proof of the completeness theorem of the theory of distributive normal forms is pointed out, and a similar completeness theorem is proved using the new definition of trivial inconsistency. 2014-11-15T19:36:50Z 2014-11-15T19:36:50Z 1997 Master Thesis Masters MSc http://hdl.handle.net/11427/9648 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Nelte, Karen Formulas of first-order logic in distributive normal form |
| thesis_degree_str | Master's |
| title | Formulas of first-order logic in distributive normal form |
| title_full | Formulas of first-order logic in distributive normal form |
| title_fullStr | Formulas of first-order logic in distributive normal form |
| title_full_unstemmed | Formulas of first-order logic in distributive normal form |
| title_short | Formulas of first-order logic in distributive normal form |
| title_sort | formulas of first order logic in distributive normal form |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/9648 |
| work_keys_str_mv | AT neltekaren formulasoffirstorderlogicindistributivenormalform |