Any ground associative-commutative theory has a finite canonical system
Identifieur interne : 00C093 ( Main/Exploration ); précédent : 00C092; suivant : 00C094Any ground associative-commutative theory has a finite canonical system
Auteurs : Paliath Narendran [États-Unis] ; Michaël Rusinowitch [France]Source :
- Journal of Automated Reasoning [ 0168-7433 ] ; 1996-08-01.
English descriptors
- KwdEn :
- Teeft :
- Algorithm, Associative path, Axiom, Binary relation, Canonical, Canonical system, Canonical systems, Commutative, Commutative semigroups, Commutativity axioms, Complete sets, Completion procedure, Computer science, Congruence classes, Congruence classes modulo, Critical pair, Critical pairs, Decidable word problem, Decision algorithms, Distributivity rule, Finite canonical system, Function symbol, Ground equations, Ground terms, Ground theory, Infinite sequence, Lecture notes, Main property, Minimal proof, Modulo, Narendran, Normal form, Paliath narendran, Petri nets, Polynomial interpretations, Proc, Reachability problem, Root symbol, Rusinowitch, Same number, Same root symbol, Several symbols, Smaller proof, Such properties, Symbolic computation, Systems modulo, Technical report, Theoretical computer science, Unifiability problem, Word problem, Word problems.
Abstract
Abstract: It is shown that theories presented by a set of ground equations with several associative-commutative (AC) symbols always admit a finite canonical system. This result is obtained through the construction of a reduction ordering that is AC-compatible and total on the set of congruence classes generated by the associativity and commutativity axioms. As far as we know, this is the first ordering with such properties when several AC-function symbols and free-function symbols are allowed. Such an ordering is also a fundamental tool for deriving a complete theorem proving strategies with built-in associative commutative unification.
Url:
DOI: 10.1007/BF00247671
Affiliations:
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This result is obtained through the construction of a reduction ordering that is AC-compatible and total on the set of congruence classes generated by the associativity and commutativity axioms. As far as we know, this is the first ordering with such properties when several AC-function symbols and free-function symbols are allowed. Such an ordering is also a fundamental tool for deriving a complete theorem proving strategies with built-in associative commutative unification.</div></front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Grand Est</li><li>Lorraine (région)</li><li>État de New York</li></region><settlement><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="États-Unis"><region name="État de New York"><name sortKey="Narendran, Paliath" sort="Narendran, Paliath" uniqKey="Narendran P" first="Paliath" last="Narendran">Paliath Narendran</name></region><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="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michaël" last="Rusinowitch">Michaël Rusinowitch</name></region><name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michaël" last="Rusinowitch">Michaël Rusinowitch</name><name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michaël" last="Rusinowitch">Michaël Rusinowitch</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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