# Formulas of first-order logic in distributive normal form

 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). Formulas of first-order logic in distributive normal form. (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. "Formulas of first-order logic in distributive normal form." 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 en_ZA 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 -
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