MoL-2011-17: The Cylindric Algebras of 4-Valued Logic

MoL-2011-17: Jacobsz, Rogier (2011) The Cylindric Algebras of 4-Valued Logic. [Report]

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In this thesis the syntax and semantics of four-valued first-order predicate logic are introduced. When we define the semantics, we use 4-cylindric set algebras. Then we define 4-cylindric algebras which are supposed to reflect the algebraic properties of this logic. We give a method for constructing 4-cylindric algebras out of cylindric algebras and prove that in fact every 4-cylindric algebra is isomorphic to a 4-cylindric algebra that is constructed in this way. It will turn out that every locally finite 4-cylindric algebra is a subdirect product of a family of 4-cylindric 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 4-cylindric algebras to 3-cylindric algebras. It turns out that every 4- cylindric algebra contains a 3-cylindric algebra as a subreduct. Moreover, every 3-cylindric algebra is isomorphic to a subreduct of some 4-cylindric algebra.

Item Type: Report
Report Nr: MoL-2011-17
Series Name: Master of Logic Thesis (MoL) Series
Year: 2011
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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