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Journal of Logic and Computation, Volume 11, Issue 5, pp. 691-700: Abstract.

Relation Algebra with Binders

Maarten Marx

Applied Logic Lab, ILLC, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands. E-mail: marx@wins.uva.nl

The language of relation algebras is expanded with variables denoting individual elements in the domain and with the [darr] binder from hybrid logic. Every elementary property of binary relations is expressible in the resulting language, something which fails for the relation algebraic language. That the new language is natural for speaking about binary relations is indicated by the fact that both Craig's Interpolation, and Beth's Definability theorems hold for its set of validities. The paper contains a number of worked examples.

Keywords: Binary relations, relation algebras, modal logic, hybrid logic, fork algebras, interpolation, Beth definability

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