InforLorV4, Main, Exploration, bibRecord, 000316

Unification and Matching in Hierarchical Combinations of Syntactic Theories

Identifieur interne : 000316 ( Main/Exploration ); précédent : 000315; suivant : 000317

Unification and Matching in Hierarchical Combinations of Syntactic Theories

Auteurs : Serdar Erbatur [Allemagne] ; Deepak Kapur [États-Unis] ; Andrew Marshall [États-Unis] ; Paliath Narendran [États-Unis] ; Christophe Ringeissen [France]

Source :

RBID : Hal:hal-01206669

Abstract

We investigate a hierarchical combination approach to the unification problem in non-disjoint unions of equational theories. In this approach, the idea is to extend a base theory with some additional axioms given by rewrite rules in such way that the unification algorithm known for the base theory can be reused without loss of completeness. Additional techniques are required to solve a combined problem by reducing it to a problem in the base theory. In this paper we show that the hierarchical combination approach applies successfully to some classes of syntactic theories, such as shallow theories since the required unification algorithms needed for the combination algorithm can always be obtained. We also consider the matching problem in syntactic extensions of a base theory. Due to the more restricted nature of the matching problem, we obtain several improvements over the unification problem.

Url:

https://hal.inria.fr/hal-01206669

DOI: 10.1007/978-3-319-24246-0_18

Affiliations:

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Le document en format XML

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<orgName>Université de Franche-Comté</orgName>
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<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.univ-fcomte.fr</ref>
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</org>
</tutelle>
<tutelle active="#struct-300261" type="indirect"><org type="institution" xml:id="struct-300261" status="VALID"><orgName>Université de Technologie de Belfort-Montbeliard</orgName>
<orgName type="acronym">UTBM</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
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<desc><address><country key="FR"></country>
</address>
</desc>
</org>
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<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
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</address>
<ref type="url">http://www.cnrs.fr/</ref>
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<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
<placeName><settlement type="city" wicri:auto="siege">Besançon</settlement>
<region type="region" nuts="2">Franche-Comté</region>
</placeName>
<orgName type="university">Université de Franche-Comté</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName>
<placeName><settlement type="city" wicri:auto="siege">Belfort</settlement>
<region type="region" nuts="2">Franche-Comté</region>
</placeName>
<orgName type="university">Université de technologie de Belfort-Montbéliard</orgName>
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<idno type="DOI">10.1007/978-3-319-24246-0_18</idno>
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<front><div type="abstract" xml:lang="en">We investigate a hierarchical combination approach to the  unification problem in non-disjoint unions of equational  theories. In this approach, the idea is to extend a base theory with  some additional axioms given by rewrite rules in such way that the  unification algorithm known for the base theory can be reused  without loss of completeness. Additional techniques are required to  solve a combined problem by reducing it to a problem in the base  theory.  In this paper we show that the hierarchical combination  approach applies successfully to some classes of syntactic theories,  such as shallow theories since the required unification algorithms  needed for the combination algorithm can always be obtained. We also  consider the matching problem in syntactic extensions of a base  theory.  Due to the more restricted nature of the matching problem,  we obtain several improvements over the unification problem.</div>
</front>
</TEI>
<affiliations><list><country><li>Allemagne</li>
<li>France</li>
<li>États-Unis</li>
</country>
<region><li>Franche-Comté</li>
<li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Belfort</li>
<li>Besançon</li>
<li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Bourgogne Franche-Comté</li>
<li>Université de Franche-Comté</li>
<li>Université de Lorraine</li>
<li>Université de technologie de Belfort-Montbéliard</li>
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</country>
<country name="États-Unis"><noRegion><name sortKey="Kapur, Deepak" sort="Kapur, Deepak" uniqKey="Kapur D" first="Deepak" last="Kapur">Deepak Kapur</name>
</noRegion>
<name sortKey="Marshall, Andrew" sort="Marshall, Andrew" uniqKey="Marshall A" first="Andrew" last="Marshall">Andrew Marshall</name>
<name sortKey="Narendran, Paliath" sort="Narendran, Paliath" uniqKey="Narendran P" first="Paliath" last="Narendran">Paliath Narendran</name>
</country>
<country name="France"><region name="Grand Est"><name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name>
</region>
</country>
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Unification and Matching in Hierarchical Combinations of Syntactic Theories

Unification and Matching in Hierarchical Combinations of Syntactic Theories

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