04535nam 22007335 450 99646527480331620200705062117.03-540-47561-310.1007/BFb0031932(CKB)1000000000233677(SSID)ssj0000324032(PQKBManifestationID)11245095(PQKBTitleCode)TC0000324032(PQKBWorkID)10304480(PQKB)10857887(DE-He213)978-3-540-47561-3(PPN)155206958(EXLCZ)99100000000023367720121227d1991 u| 0engurnn|008mamaatxtccrInstantiation Theory[electronic resource] On the Foundations of Automated Deduction /by James G. Williams1st ed. 1991.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1991.1 online resource (VIII, 136 p.) Lecture Notes in Artificial Intelligence ;518Bibliographic Level Mode of Issuance: Monograph3-540-54333-3 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.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.Lecture Notes in Artificial Intelligence ;518Artificial intelligenceComputersSoftware engineeringMathematical logicComputer science—MathematicsAlgorithmsArtificial Intelligencehttps://scigraph.springernature.com/ontologies/product-market-codes/I21000Theory of Computationhttps://scigraph.springernature.com/ontologies/product-market-codes/I16005Software Engineering/Programming and Operating Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/I14002Mathematical Logic and Formal Languageshttps://scigraph.springernature.com/ontologies/product-market-codes/I16048Symbolic and Algebraic Manipulationhttps://scigraph.springernature.com/ontologies/product-market-codes/I17052Algorithm Analysis and Problem Complexityhttps://scigraph.springernature.com/ontologies/product-market-codes/I16021Artificial intelligence.Computers.Software engineering.Mathematical logic.Computer science—Mathematics.Algorithms.Artificial Intelligence.Theory of Computation.Software Engineering/Programming and Operating Systems.Mathematical Logic and Formal Languages.Symbolic and Algebraic Manipulation.Algorithm Analysis and Problem Complexity.511.3Williams James Gauthttp://id.loc.gov/vocabulary/relators/aut8470BOOK996465274803316Instantiation Theory2831335UNISA