Relation Algebra with Binders
Maarten Marx
Abstract:
The language of relation algebras is expanded with variables denoting
individual elements in the domain and with the downarrow 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 theorem hold for its
set of validities. The paper contains a number of worked out
examples.
Keyword(s): Binary relations, relation algebras, modal logic, hybrid
logic, fork algebras, interpolation, Beth definabili