Reductions and Algorithms for Lattices with Complements
نویسنده
چکیده
We present tractable algorithms for deciding the universal theories of lattices with different notions of complementation by reduction to more standard procedures. The reductions use basic structural properties of lattices. For Boolean algebras, generalised Boolean algebras and atomic distributive lattices we reduce to SAT-procedures. For Brouwerian algebras we reduce to the uniform word problem for distributive lattices. A side effect is a reduction for Boolean rings to its canonical term rewriting system instead of using Gröbner bases. The resulting procedures are simple, modular and robust. Applications include proof support for set-based program development, spatial reasoning, rough set analysis and dependency analysis in programs and databases.
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