MoL201117: Jacobsz, Rogier (2011) The Cylindric Algebras of 4Valued Logic. [Report]

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Abstract
In this thesis the syntax and semantics of fourvalued firstorder predicate logic are introduced. When we define the semantics, we use 4cylindric set algebras. Then we define 4cylindric algebras which are supposed to reflect the algebraic properties of this logic. We give a method for constructing 4cylindric algebras out of cylindric algebras and prove that in fact every 4cylindric algebra is isomorphic to a 4cylindric algebra that is constructed in this way. It will turn out that every locally finite 4cylindric algebra is a subdirect product of a family of 4cylindric set algebras. This result will be used in order to prove a completeness theorem with respect to a proof system we introduce. At last, we compare 4cylindric algebras to 3cylindric algebras. It turns out that every 4 cylindric algebra contains a 3cylindric algebra as a subreduct. Moreover, every 3cylindric algebra is isomorphic to a subreduct of some 4cylindric algebra.
Item Type:  Report 

Report Nr:  MoL201117 
Series Name:  Master of Logic Thesis (MoL) Series 
Year:  2011 
Date Deposited:  12 Oct 2016 14:38 
Last Modified:  12 Oct 2016 14:38 
URI:  https://eprints.illc.uva.nl/id/eprint/862 
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