Combining Nonstably Infinite Theories
Identifieur interne : 005522 ( Main/Exploration ); précédent : 005521; suivant : 005523Combining Nonstably Infinite Theories
Auteurs : Cesare Tinelli [États-Unis] ; Calogero G. Zarba [États-Unis]Source :
- Journal of Automated Reasoning [ 0168-7433 ] ; 2005-04-01.
English descriptors
Abstract
Abstract: The Nelson–Oppen combination method combines decision procedures for first-order theories over disjoint signatures into a single decision procedure for the union theory. In order to be correct, the method requires that the component theories be stably infinite. This restriction makes the method inapplicable to many interesting theories such as, for instance, theories having only finite models. In this paper, we describe two extensions of the Nelson–Oppen method that address the problem of combining theories that are not stably infinite. In our extensions, the component decision procedures exchange not only equalities between shared variables but also certain cardinality constraints. Applications of our results include the combination of theories having only finite models, as well as the combination of nonstably infinite theories with the theory of equality, the theories of total and partial orders, and the theory of lattices with maximum and minimum.
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DOI: 10.1007/s10817-005-5204-9
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In order to be correct, the method requires that the component theories be stably infinite. This restriction makes the method inapplicable to many interesting theories such as, for instance, theories having only finite models. In this paper, we describe two extensions of the Nelson–Oppen method that address the problem of combining theories that are not stably infinite. In our extensions, the component decision procedures exchange not only equalities between shared variables but also certain cardinality constraints. Applications of our results include the combination of theories having only finite models, as well as the combination of nonstably infinite theories with the theory of equality, the theories of total and partial orders, and the theory of lattices with maximum and minimum.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>Iowa</li><li>Nouveau-Mexique</li></region><settlement><li>Iowa City</li></settlement><orgName><li>Université de l'Iowa</li></orgName></list><tree><country name="États-Unis"><region name="Iowa"><name sortKey="Tinelli, Cesare" sort="Tinelli, Cesare" uniqKey="Tinelli C" first="Cesare" last="Tinelli">Cesare Tinelli</name></region><name sortKey="Tinelli, Cesare" sort="Tinelli, Cesare" uniqKey="Tinelli C" first="Cesare" last="Tinelli">Cesare Tinelli</name><name sortKey="Zarba, Calogero G" sort="Zarba, Calogero G" uniqKey="Zarba C" first="Calogero G." last="Zarba">Calogero G. Zarba</name><name sortKey="Zarba, Calogero G" sort="Zarba, Calogero G" uniqKey="Zarba C" first="Calogero G." last="Zarba">Calogero G. Zarba</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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