The Cylindric Algebras of 4-Valued Logic
Rogier Jacobsz
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.