On the computational complexity of algebra on lattices
SIAM Journal on Computing
Ordered chaining calculi for first-order theories of transitive relations
Journal of the ACM (JACM)
Resolution Methods for the Decision Problem
Resolution Methods for the Decision Problem
Tarskian Set Constraints Are in NEXPTIME
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Encoding two-valued nonclassical logics in classical logic
Handbook of automated reasoning
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
The Two-Variable Guarded Fragment with Transitive Relations
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Representation Theorems and Theorem Proving in Non-Classical Logics
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
On the Decision Problem for the Guarded Fragment with Transitivity
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
On unification for bounded distributive lattices
ACM Transactions on Computational Logic (TOCL)
Automated theorem proving by resolution in non-classical logics
Annals of Mathematics and Artificial Intelligence
On the refutational completeness of signed binary resolution and hyperresolution
Fuzzy Sets and Systems
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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We establish a link between the satisfiability of universal sentences with respect to classes of distributive lattices with operators and their satisfiability with respect to certain classes of relational structures. This justifies a method for structure-preserving translation to clause form of universal sentences in such classes of algebras. We show that refinements of resolution yield decision procedures for the universal theory of some such classes. In particular, we obtain exponential space and time decision procedures for the universal clause theory of (i) the class of all bounded distributive lattices with operators satisfying a set of (generalized) residuation conditions, and (ii) the class of all bounded distributive lattices with operators, and a doubly-exponential time decision procedure for the universal clause theory of the class of all Heyting algebras.