A Proof Theory for General Unification

W. Snyder (Autor)

Buch | Softcover

178 Seiten

2012 | Softcover reprint of the original 1st ed. 1991
Springer-Verlag New York Inc.
978-1-4612-6758-4 (ISBN)

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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.

1: Introduction.- 2: Preview.- 3: Preliminaries.- 3.1 Algebraic Background.- 3.2 Substitutions.- 3.3 Unification by Transformations on Systems.- 3.4 Equational Logic.- 3.5 Term Rewriting.- 3.6 Completion of Equational Theories.- 4: E-Unification.- 4.1 Basic Definitions and Results.- 4.2 Methods for E-Unification.- 5: E-Unification via Transformations.- 5.1 The Set of Transformations BT.- 5.2 Soundness of the Set BT.- 5.3 Completeness of the Set BT.- 6: An Improved Set of Transformations.- 6.1 Ground Church-Rosser Systems.- 6.2 Completeness of the Set T.- 6.3 Surreduction.- 6.4 Completeness of the Set T Revisited.- 6.5 Relaxed Paramodulation.- 6.6 Previous Work.- 6.7 Eager Variable Elimination.- 6.8 Current and Future Work.- 6.9 Conclusion.- 7: Higher Order Unification.- 7.1 Preliminaries.- 7.2 Higher Order Unification via Transformations.- 7.3 Huet’s Procedure Revisited.- 7.4 Conclusion.- 8: Conclusion.- Appendices.

Erscheint lt. Verlag	30.9.2012
Reihe/Serie	Progress in Computer Science and Applied Logic ; 11
Zusatzinfo	VII, 178 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4612-6758-7 / 1461267587
ISBN-13	978-1-4612-6758-4 / 9781461267584
Zustand	Neuware