Abstract
Characterizations are given for the classes of partial subalgebras of distributive lattices, boolean algebras and Heyting algebras. Thereby, complexity results are obtained for the satisfiability of quantifier-free first-order sentences in these classes. Satisfiability is NP-complete for distributive lattices and boolean algebras, and for Heyting algebras is PSPACE-complete. Consequently, the universal theory of distributive lattices and of boolean algebras is co-NP-complete and the universal theory of Heyting algebras is PSPACE-complete.
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