Handbook of theoretical computer science (vol. B)
Handbook of theoretical computer science (vol. B)
Theory of partial-order programming
Science of Computer Programming
An application of lattice theory to knowledge representation
Theoretical Computer Science - Modern algebra and its applications
Complexity of Lattice Problems
Complexity of Lattice Problems
Hierarchic reasoning in local theory extensions
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
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We present a decision procedure for the quantifier-free satisfiability problem of the language BLmf of bounded lattices with monotone unary functions. The language contains the predicates = and ≤, as well as the operators⊓and ⊔ over terms which may involve uninterpreted unary function symbols. The language also contains predicates for expressing increasing and decreasing monotonicity of functions, as well as a predicate for pointwise function comparison. Our decision procedure runs in polynomial time ${\mathcal{O}(m^{4})}$ for normalized conjunctions of m literals, thus entailing that the quantifier-free satisfiability problem for BLmf is $\mathcal{NP}$-complete. Furthermore, our decision procedure can be used to decide the quantifier-free satisfiability problem for the language CLmf of complete lattices with monotone functions. This allows us to conclude that the languages BLmf and CLmf are equivalent for quantifier-free formulae.