Expressive Power and Complexity in Algebraic Logic (1997)
| Venue: | Journal of Logic and Computation |
| Citations: | 17 - 2 self |
BibTeX
@ARTICLE{Hirsch97expressivepower,
author = {Robin Hirsch},
title = {Expressive Power and Complexity in Algebraic Logic},
journal = {Journal of Logic and Computation},
year = {1997},
volume = {7},
pages = {309--351}
}
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Abstract
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 generalise known complexity results to a range of other algebraic logics. In particular a number of relation algebras are shown to have intractable network satisfaction problems. 1 Introduction A basic problem in theoretical computing and applied logic is to select and evaluate the ideal formalism to represent and reason about a given application. Many different formalisms are adopted: classical first-order logic, modal and temporal logics (either...
