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| In [[computer science]], '''term indexing''' is the task of creating an [[index (search engine)|index]] of terms and clauses in a collection.
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| Many operations in automatic [[Automated theorem prover|theorem prover]]s require search in huge
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| collections of terms and clauses. Such operations typically fall into
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| the following scheme. Given a collection <math>S</math> of terms (clauses) and a query
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| term (clause) <math>q</math>, find in <math>S</math> some/all terms <math>t</math> related to <math>q</math> according to a
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| certain retrieval condition. Most interesting retrieval conditions
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| are formulated as existence of a substitution that relates in a special
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| way the query and the retrieved objects <math>t</math>. Here is a list of retrieval
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| conditions frequently used in provers:
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| * term <math>q</math> is unifiable with term <math>t</math>, i.e., there exists a substitution <math> \theta </math>, such that <math>q\theta</math> = <math>t\theta</math>
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| * term <math>t</math> is an instance of <math>q</math>, i.e., there exists a substitution <math>\theta</math>, such that <math>q\theta</math> = <math>t</math>
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| * term <math>t</math> is a generalisation of <math>q</math>, i.e., there exists a substitution <math>\theta</math>, such that <math>q</math> = <math>t\theta</math>
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| * clause <math>q</math> subsumes clause <math>t</math>, i.e., there exists a substitution <math>\theta</math>, such that <math>q\theta</math> is a subset/submultiset of <math>t</math>
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| * clause <math>q</math> is subsumed by <math>t</math>, i.e., there exists a substitution <math>\theta</math>, such that <math>t\theta</math> is a subset/submultiset of <math>q</math>
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| More often than not, we are actually interested in finding the appropriate
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| substitutions explicitly, together with the retrieved terms <math>t</math>,
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| rather than just in establishing existence of such substitutions.
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| Very often the sizes of term sets to be searched are large,
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| the retrieval calls are frequent and the retrieval condition test
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| is rather complex. In such situations linear search in <math>S</math>, when the retrieval
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| condition is tested on every term from <math>S</math>, becomes prohibitively costly.
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| To overcome this problem, special data structures, called ''indexes'', are
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| designed in order to support fast retrieval. Such data structures,
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| together with the accompanying algorithms for index maintenance
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| and retrieval, are called ''term indexing techniques''.
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| ==Classic indexing techniques==
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| * [[discrimination tree]]s
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| * [[substitution tree]]s
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| * [[path indexing]]
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| ==Modern indexing techniques==
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| * [[feature vector indexing]]
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| * [[code tree]]s
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| * [[context tree]]s
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| * [[relational path indexing]]
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| ==Further reading==
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| * P. Graf, Term Indexing, Lecture Notes in Computer Science 1053, 1996 (slightly outdated overview)
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| * R. Sekar and I.V. Ramakrishnan and A. Voronkov, Term Indexing, in A. Robinson and A. Voronkov, editors, [[Handbook of Automated Reasoning]], volume 2, 2001 (recent overview)
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| * W. W. McCune, Experiments with Discrimination-Tree Indexing and Path Indexing for Term Retrieval, Journal of Automated Reasoning, 9(2), 1992
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| * P. Graf, Substitution Tree Indexing, Proc. of RTA, Lecture Notes in Computer Science 914, 1995
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| * M. Stickel, The Path Indexing Method for Indexing Terms, Tech. Rep. 473, [[Artificial Intelligence Center]], [[SRI International]], 1989
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| * S. Schulz, Simple and Efficient Clause Subsumption with Feature Vector Indexing, Proc. of IJCAR-2004 workshop ESFOR, 2004
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| * A. Riazanov and A. Voronkov, Partially Adaptive Code Trees, Proc. JELIA, Lecture Notes in Artificial Intelligence 1919, 2000
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| * H. Ganzinger and R. Nieuwenhuis and P. Nivela, Fast Term Indexing with Coded Context Trees, Journal of Automated Reasoning, 32(2), 2004
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| * A. Riazanov and A. Voronkov, Efficient Instance Retrieval with Standard and Relational Path Indexing, Information and Computation, 199(1–2), 2005
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| {{DEFAULTSORT:Term Indexing}}
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| [[Category:Searching]]
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| [[fr:Index terminologique]]
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| [[pl:Indeksowanie termów]]
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