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Lecture Notes in Artificial Intelligence

Instantiation Theory

On the Foundations of Automated Deduction

Authors: Williams, James G.

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About this book

Instantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic programming systems. Instantiation theory is the study of instantiation in an abstract context that is applicable to most commonly studied logical formalisms. The volume begins with a survey of general approaches to the study of instantiation, as found in tree systems, order-sorted algebras, algebraic theories, composita, and instantiation systems. A classification of instantiation systems is given, based on properties of substitutions, degree of type strictness, and well-foundedness of terms. Equational theories and the use of typed variables are studied in terms of quotient homomorphisms and embeddings, respectively. Every instantiation system is a quotient system of a subsystem of first-order term instantiation. The general unification algorithm is developed as an application of the basic theory. Its soundness is rigorously proved, and its completeness and efficiency are verfied for certain classes of instantiation systems. Appropriate applications of the algorithm include unification of first-order terms, order-sorted terms, and first-order formulas modulo alpha-conversion, as well as equational unification using simple congruences.

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-540-47561-3
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-540-54333-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Instantiation Theory
Book Subtitle
On the Foundations of Automated Deduction
Authors
Series Title
Lecture Notes in Artificial Intelligence
Series Volume
518
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47561-3
DOI
10.1007/BFb0031932
Softcover ISBN
978-3-540-54333-6
Edition Number
1
Number of Pages
VIII, 136
Topics