Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 ll 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 ll as a predicate for pointwise function comparison.#R##N##R##N#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.
['Domenico Cantone', 'Calogero G. Zarba']
I am writing a research paper on a idea A decision procedure for monotone functions over bounded and complete lattices
[{"from": "human", "value": "I am writing a research paper on a idea A decision procedure for monotone functions over bounded and complete lattices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 \u2264, as ll as the operators\u2293and \u2294 over terms which may involve uninterpreted unary function symbols. The language also contains predicates for expressing increasing and decreasing monotonicity of functions, as ll as a predicate for pointwise function comparison.#R##N##R##N#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."}]