A Proof Theory For General Unification
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A Proof Theory for General Unification
Author: W. Snyder
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.
Handbook of Proof Theory
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.