130 research outputs found
Independence-friendly cylindric set algebras
Independence-friendly logic is a conservative extension of first-order logic
that has the same expressive power as existential second-order logic. In her
Ph.D. thesis, Dechesne introduces a variant of independence-friendly logic
called IFG logic. We attempt to algebraize IFG logic in the same way that
Boolean algebra is the algebra of propositional logic and cylindric algebra is
the algebra of first-order logic.
We define independence-friendly cylindric set algebras and prove two main
results. First, every independence-friendly cylindric set algebra over a
structure has an underlying Kleene algebra. Moreover, the class of such
underlying Kleene algebras generates the variety of all Kleene algebras. Hence
the equational theory of the class of Kleene algebras that underly an
independence-friendly cylindric set algebra is finitely axiomatizable. Second,
every one-dimensional independence-friendly cylindric set algebra over a
structure has an underlying monadic Kleene algebra. However, the class of such
underlying monadic Kleene algebras does not generate the variety of all monadic
Kleene algebras. Finally, we offer a conjecture about which subvariety of
monadic Kleene algebras the class of such monadic Kleene algebras does
generate.Comment: 42 pages. Submitted to the Logic Journal of the IGPL. See also
http://math.colgate.edu/~amann
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
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