A Decision Procedure for Monotone Functions over Bounded and Complete Lattices

  • Domenico Cantone
  • Calogero G. Zarba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4342)


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.


Partial Order Model Check Monotone Function Bounded Lattice Inference Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Domenico Cantone
    • 1
  • Calogero G. Zarba
    • 2
  1. 1.Università degli Studi di CataniaItaly
  2. 2.Universität des SaarlandesGermany

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