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Instantiation Theory

  • Kartonierter Einband
  • 148 Seiten
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Instantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic ... Weiterlesen
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Beschreibung

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.

This monograph presents a new, general algorithm for use in building theorem provers and logic programming systems. The algorithm is based on a theory that may be developed into a general theory of logics. Appropriate applications of the algorithm and its underlying theory are given.

Klappentext

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.



Inhalt
Background.- General approaches to instantiation.- Classification properties.- Homomorphisms.- Construct bases.- Unification - an algorithm and its soundness.- Term-implementation and completeness.- Implementation and computational complexity.- Related issues not addressed.

Produktinformationen

Titel: Instantiation Theory
Untertitel: On the Foundations of Automated Deduction
Autor:
EAN: 9783540543336
ISBN: 3540543333
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Anzahl Seiten: 148
Gewicht: 236g
Größe: H235mm x B155mm x T8mm
Jahr: 1991
Untertitel: Englisch
Auflage: 1991

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