In this paper we determine the complexity of a broad class of problems that
extends the temporal constraint satisfaction problems. To be more precise we
study the problems Poset-SAT(Φ), where Φ is a given set of
quantifier-free ≤-formulas. An instance of Poset-SAT(Φ) consists of
finitely many variables x1,…,xn and formulas
ϕi(xi1,…,xik) with ϕi∈Φ; the question is
whether this input is satisfied by any partial order on x1,…,xn or
not. We show that every such problem is NP-complete or can be solved in
polynomial time, depending on Φ. All Poset-SAT problems can be formalized
as constraint satisfaction problems on reducts of the random partial order. We
use model-theoretic concepts and techniques from universal algebra to study
these reducts. In the course of this analysis we establish a dichotomy that we
believe is of independent interest in universal algebra and model theory.Comment: 29 page