Formulas of first-order logic in distributive normal form

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dc.contributor.advisorBrink, Chrisen_ZA
dc.contributor.advisorKieseppä, Ilkkaen_ZA
dc.contributor.authorNelte, Karenen_ZA
dc.date.accessioned2014-11-15T19:36:50Z
dc.date.available2014-11-15T19:36:50Z
dc.date.issued1997en_ZA
dc.descriptionBibliography: leaves 140-143.en_ZA
dc.description.abstractIt 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.identifier.apacitationNelte, 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/11427/9648en_ZA
dc.identifier.chicagocitationNelte, 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/11427/9648en_ZA
dc.identifier.citationNelte, K. 1997. Formulas of first-order logic in distributive normal form. University of Cape Town.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
dc.identifier.urihttp://hdl.handle.net/11427/9648
dc.identifier.vancouvercitationNelte 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/11427/9648en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleFormulas of first-order logic in distributive normal formen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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