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010   $a3-540-47561-3
024 7 $a10.1007/BFb0031932
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035   $a(PQKBTitleCode)TC0000324032
035   $a(PQKBWorkID)10304480
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035   $a(DE-He213)978-3-540-47561-3
035   $a(PPN)155206958
035   $a(EXLCZ)991000000000233677
100   $a20121227d1991      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aInstantiation Theory$b[electronic resource] $eOn the Foundations of Automated Deduction /$fby James G. Williams
205   $a1st ed. 1991.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1991.
215   $a1 online resource (VIII, 136 p.) 
225 1 $aLecture Notes in Artificial Intelligence ;$v518
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-54333-3 
327   $aBackground -- 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.
330   $aInstantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic programming systems. Instantiation theory is the study of instantiation in an abstract context that is applicable to most commonly studied logical formalisms. The volume begins with a survey of general approaches to the study of instantiation, as found in tree systems, order-sorted algebras, algebraic theories, composita, and instantiation systems. A classification of instantiation systems is given, based on properties of substitutions, degree of type strictness, and well-foundedness of terms. Equational theories and the use of typed variables are studied in terms of quotient homomorphisms and embeddings, respectively. Every instantiation system is a quotient system of a subsystem of first-order term instantiation. The general unification algorithm is developed as an application of the basic theory. Its soundness is rigorously proved, and its completeness and efficiency are verfied for certain classes of instantiation systems. Appropriate applications of the algorithm include unification of first-order terms, order-sorted terms, and first-order formulas modulo alpha-conversion, as well as equational unification using simple congruences.
410  0$aLecture Notes in Artificial Intelligence ;$v518
606   $aArtificial intelligence
606   $aComputers
606   $aSoftware engineering
606   $aMathematical logic
606   $aComputer science?Mathematics
606   $aAlgorithms
606   $aArtificial Intelligence$3https://scigraph.springernature.com/ontologies/product-market-codes/I21000
606   $aTheory of Computation$3https://scigraph.springernature.com/ontologies/product-market-codes/I16005
606   $aSoftware Engineering/Programming and Operating Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/I14002
606   $aMathematical Logic and Formal Languages$3https://scigraph.springernature.com/ontologies/product-market-codes/I16048
606   $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052
606   $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021
615  0$aArtificial intelligence.
615  0$aComputers.
615  0$aSoftware engineering.
615  0$aMathematical logic.
615  0$aComputer science?Mathematics.
615  0$aAlgorithms.
615 14$aArtificial Intelligence.
615 24$aTheory of Computation.
615 24$aSoftware Engineering/Programming and Operating Systems.
615 24$aMathematical Logic and Formal Languages.
615 24$aSymbolic and Algebraic Manipulation.
615 24$aAlgorithm Analysis and Problem Complexity.
676   $a511.3
700   $aWilliams$b James G$4aut$4http://id.loc.gov/vocabulary/relators/aut$08470
906   $aBOOK
912   $a996465274803316
996   $aInstantiation Theory$92831335
997   $aUNISA