TY  - BOOK
AU  - Williams,James G.
ED  - SpringerLink (Online service)
TI  - Instantiation Theory: On the Foundations of Automated Deduction 
T2  - Lecture Notes in Computer Science, Lectures Notes in Artificial Intelligence,
SN  - 9783540475613
AV  - Q334-342 
U1  - 006.3 23
PY  - 1991///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Computer science
KW  - Computer software
KW  - Algebra
KW  - Data processing
KW  - Artificial intelligence
KW  - Logic, Symbolic and mathematical
KW  - Computer Science
KW  - Artificial Intelligence (incl. Robotics)
KW  - Mathematical Logic and Formal Languages
KW  - Symbolic and Algebraic Manipulation
KW  - Algorithm Analysis and Problem Complexity
KW  - Programming Techniques
KW  - Mathematical Logic and Foundations
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0031932
ER  -