MoL-2011-17: Jacobsz, Rogier (2011) The Cylindric Algebras of 4-Valued Logic. [Report]
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Abstract
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 |
| URI: | https://eprints.illc.uva.nl/id/eprint/862 |
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