000 03669nam a22005775i 4500
001 978-3-540-47561-3
003 DE-He213
005 20160624102024.0
007 cr nn 008mamaa
008 121227s1991 gw | s |||| 0|eng d
020 _a9783540475613
_9978-3-540-47561-3
024 7 _a10.1007/BFb0031932
_2doi
050 4 _aQ334-342
050 4 _aTJ210.2-211.495
072 7 _aUYQ
_2bicssc
072 7 _aTJFM1
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aWilliams, James G.
_eauthor.
245 1 0 _aInstantiation Theory
_h[electronic resource] :
_bOn the Foundations of Automated Deduction /
_cby James G. Williams.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1991.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1991.
300 _aVIII, 136 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Computer Science, Lectures Notes in Artificial Intelligence,
_x0302-9743 ;
_v518
505 0 _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.
520 _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.
650 0 _aComputer science.
650 0 _aComputer software.
650 0 _aAlgebra
_xData processing.
650 0 _aArtificial intelligence.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aComputer Science.
650 2 4 _aArtificial Intelligence (incl. Robotics).
650 2 4 _aMathematical Logic and Formal Languages.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aAlgorithm Analysis and Problem Complexity.
650 2 4 _aProgramming Techniques.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540543336
786 _dSpringer
830 0 _aLecture Notes in Computer Science, Lectures Notes in Artificial Intelligence,
_x0302-9743 ;
_v518
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0031932
942 _2EBK6109
_cEBK
999 _c35403
_d35403