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Mathematical Logic Quarterly, 1992
AbstractWe show that a coherent theory of partially ordered connectives can be developed along the same line as partially ordered quantification. We estimate the expressive power of various partially ordered connectives and use methods like Ehrenfeucht games and infinitary logic to get various undefinability results.
Gabriel Sandu, Jouko Väänänen
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AbstractWe show that a coherent theory of partially ordered connectives can be developed along the same line as partially ordered quantification. We estimate the expressive power of various partially ordered connectives and use methods like Ehrenfeucht games and infinitary logic to get various undefinability results.
Gabriel Sandu, Jouko Väänänen
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Partial Orderings in Chemistry
Journal of Chemical Information and Computer Sciences, 1997The cosmopolitan relevance of partially ordered mathematical structures in chemistry is argued. Many examples are briefly noted, including those involving chemical periodicities, reactivities, aromaticities, electronegativities, molecular branching, molecular shapes, symmetries, complexities, curve fittings, and more.
Douglas J. Klein, Darko Babic
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Canadian Journal of Mathematics, 1968
Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering.
Dean, R. A., Keller, G.
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Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering.
Dean, R. A., Keller, G.
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ACM Transactions on Database Systems, 2023
Partial order multiway search(POMS) is a fundamental problem that finds applications in crowdsourcing, distributed file systems, software testing, and more. This problem involves an interaction between an algorithm 𝒜 and an oracle, conducted on a directed acyclic graph 𝒢 known to both parties.
Shangqi Lu +3 more
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Partial order multiway search(POMS) is a fundamental problem that finds applications in crowdsourcing, distributed file systems, software testing, and more. This problem involves an interaction between an algorithm 𝒜 and an oracle, conducted on a directed acyclic graph 𝒢 known to both parties.
Shangqi Lu +3 more
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18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings., 2003
We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and trees in terms of rank functions that are versions of Cantor-Bendixson rank. We prove that automatic linear orders and automatic trees have finite rank.
Bakhadyr Khoussainov +2 more
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We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and trees in terms of rank functions that are versions of Cantor-Bendixson rank. We prove that automatic linear orders and automatic trees have finite rank.
Bakhadyr Khoussainov +2 more
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The Partial Ordering on the Automorphism Group of the Countable Generic Partial Order
Order, 2009The countable generic partial order \((P,\leq)\) is defined by using the well-known Fraïssé's Theorem. This paper deals with the structure \((G,\circ,\leq)\), where \((G,\circ)=\text{Aut}(P,\leq)\) and \(\leq\) is the pointwise ordering on \(G\). It is shown that \((G,\leq)\) is elementarily equivalent to \((P,\leq)\) itself and, more generally, that \(
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ACM SIGIR Forum, 1989
In this paper we show how to maintain a partially-ordered hierarchy of patterns by subpattern-of for efficient associative retrieval. The techniques described here are most applicable for databases of complex data structures such as graphs or matrices as opposed to simple data structures such as relations, sets, lists or frames that are seen in most ...
Cathi Colin, Robert Levinson
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In this paper we show how to maintain a partially-ordered hierarchy of patterns by subpattern-of for efficient associative retrieval. The techniques described here are most applicable for databases of complex data structures such as graphs or matrices as opposed to simple data structures such as relations, sets, lists or frames that are seen in most ...
Cathi Colin, Robert Levinson
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Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89, 1989
We present a randomized algorithm which uses O(n(log n)1/3) expected comparisons to verify that a given partial order holds on n elements from an unknown total order.
Claire Kenyon-Mathieu, Valerie King
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We present a randomized algorithm which uses O(n(log n)1/3) expected comparisons to verify that a given partial order holds on n elements from an unknown total order.
Claire Kenyon-Mathieu, Valerie King
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Partial Orders on Weak Orders Convex Subsets
Order, 2000Let \(P\) and \(H\) be finite partially ordered sets (orders, for short) and \(\varphi \) be a mapping of \(P\) into the set of all nonempty convex connected subsets of \(H\).
Haiko Müller, Jean-Xavier Rampon
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