Expressive power and complexity in algebraic logic
Robin Hirsch · Journal of Logic and Computation · 1997
Two complexity problems in algebraic logic are surveyed: the satisfaction problem and the network satisfaction problem. Various complexity results are collected here and some new ones are derived. Many examples are given. The network satisfaction problem for most cylindric algebras of dimension four or more is shown to be intractable. Complexity is tied-in with the expressivity of a relation algebra. Expressivity and complexity are analysed in the context of homogeneous representations. The model-theoretic notion of interpretation is used to generalize known complexity results to a range of other algebraic logics. In particular a number of relation algebras arc shown to have intractable network satisfaction problems.