A Proof Theory for General Unification

  • Wayne Snyder

Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 11)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Wayne Snyder
    Pages 1-6
  3. Wayne Snyder
    Pages 7-16
  4. Wayne Snyder
    Pages 17-48
  5. Wayne Snyder
    Pages 49-60
  6. Wayne Snyder
    Pages 61-82
  7. Wayne Snyder
    Pages 83-122
  8. Wayne Snyder
    Pages 123-153
  9. Wayne Snyder
    Pages 154-155
  10. Back Matter
    Pages 157-178

About this book

Introduction

In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig­ inated by Herbrand and developed in the case of standard first-order unifi­ cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con­ verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher­ order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand­ Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi­ cation problems.

Keywords

algebra logic proof proof theory

Authors and affiliations

  • Wayne Snyder
    • 1
  1. 1.Department of Computer ScienceBoston UniversityBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0435-0
  • Copyright Information Birkhäuser Boston 1991
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6758-4
  • Online ISBN 978-1-4612-0435-0
  • About this book