Formulas of first-order logic in distributive normal form

 

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dc.contributor.advisor Brink, Chris en_ZA
dc.contributor.advisor Kieseppä, Ilkka en_ZA
dc.contributor.author Nelte, Karen en_ZA
dc.date.accessioned 2014-11-15T19:36:50Z
dc.date.available 2014-11-15T19:36:50Z
dc.date.issued 1997 en_ZA
dc.identifier.citation Nelte, K. 1997. Formulas of first-order logic in distributive normal form. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/9648
dc.description Bibliography: leaves 140-143. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.title Formulas of first-order logic in distributive normal form en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Nelte, K. (1997). <i>Formulas of first-order logic in distributive normal form</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/9648 en_ZA
dc.identifier.chicagocitation Nelte, Karen. <i>"Formulas of first-order logic in distributive normal form."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1997. http://hdl.handle.net/11427/9648 en_ZA
dc.identifier.vancouvercitation Nelte K. Formulas of first-order logic in distributive normal form. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1997 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9648 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Nelte, Karen AB - 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. DA - 1997 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1997 T1 - Formulas of first-order logic in distributive normal form TI - Formulas of first-order logic in distributive normal form UR - http://hdl.handle.net/11427/9648 ER - en_ZA


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