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Proposition
"... There are many relations known among the entries of Pascal's triangle. In [1], Hoggatt discusses the relation between the Fibonacci numbers and Pascal's triangle. He also gives several references to other related works. Here, we propose to show a relation between the triangle and the Ferma ..."
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and the Fermat numbers f; = 2 2 ' + 1 for i = 0, 7, 2, •• •. Let c(n,j) be Pascal's triangle, where n represents the row index and / the column index, both indices starting at zero. Let aIn] be the sequence of numbers constructed from Pascal's triangle as follows: construct a new Pascal
Proposition
"... Appendix I Lie triple systems in compact semisimple Lie algebras The elementary theory of Lie triple systems is not easily found in the literature, and for this reason we present a brief self contained treatment of some parts of the theory that are relevant for this paper. Let G be a finite dimensio ..."
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dimensional Lie algebra over Â such that the Killing form B is G negative definite. It is known that if G is any connected Lie group with Lie algebra G, then G is compact (See for example Proposition 6.6 and Theorem 6.9 of ([H, pp. 132133]). A subspace W of G is called a Lie triple system in G if [X, [Y, Z
On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals
 ARTIFICIAL INTELLIGENCE
, 1992
"... We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or ..."
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Cited by 215 (11 self)
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We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated
The stages of economic growth.
 Economic History Review , 2nd series 12,
, 1959
"... JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about J ..."
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Cited by 297 (0 self)
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JSTOR, please contact support@jstor.org. economic history. The form of this generalization is a set of stages of growth, which can be designated as follows: the traditional society; the preconditions for takeoff; the takeoff; the drive to maturity; the age of high mass consumption. Beyond the age
Propositions as Sessions
, 2012
"... Continuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), by Honda, Kubo, and Va ..."
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Cited by 37 (3 self)
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Continuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), by Honda, Kubo
Realtime logics: complexity and expressiveness
 INFORMATION AND COMPUTATION
, 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
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Cited by 252 (16 self)
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The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via
Accepted on proposition of the following jury:
, 2009
"... geometry of oppositions, nopposition, square of opposition, logical square, logical hexagon, logical bisimplexes, logical polysimplexes, contradiction, modal logic, concept, spatial logics, ndimensional geometry, central symmetry, simplexes, Aristotelian p qsemantics, Aristotelian p qlattice, ..."
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geometry of oppositions, nopposition, square of opposition, logical square, logical hexagon, logical bisimplexes, logical polysimplexes, contradiction, modal logic, concept, spatial logics, ndimensional geometry, central symmetry, simplexes, Aristotelian p qsemantics, Aristotelian p qlattice, conceptual spaces. Summary: The present work is devoted to the exploration of some formal possibilities suggesting, since some years, the possibility to elaborate a new, whole geometry, relative to the concept of “opposition”. The latter concept is very important and vast (as for its possible applications), both for philosophy and science and it admits since more than two thousand years a standard logical theory, Aristotle’s “opposition theory”, whose culminating formal point is the so called “square of opposition”. In some sense, the whole present enterprise consists in discovering and ordering geometrically an infinite amount of “avatars ” of this traditional square structure (also called “logical square ” or “Aristotle’s square”). The results obtained here go even beyond the most optimistic previous expectations, for it turns out that such a geometry exists indeed and offers to science many new conceptual insights and formal tools.
On the Syntactic Marking of Presupposed Open Propositions
 Proceedings of the 22nd Annual Meeting of the Chicago Linguistic Society
, 1986
"... this paper, more specifically a subset of the inferences that correlate with the syntactic form of a sentence uttered. Beginning with the early functional syntax studies by Kuno, Bolinger, and others more than a decade ago, a good deal of research has been carried out that shows that particular synt ..."
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Cited by 89 (2 self)
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to investigate the possibility that there do exist general principles underlying such correlations, perhaps of a universal nature. In what follows, I shall very tentatively propose one possible universal generalization concerning syntactic form and nontruthconditional understanding. And my tentativeness
On Russellian Propositions
"... This paper discusses some structural conditions under which Russellian propositions in the sense of J. Barwise and J. Etchemendy [2] are paradoxical, and the computational complexity of the problems whether or not Russellian proposition is paradoxical, intrinsically paradoxical, and classical. 1 Int ..."
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This paper discusses some structural conditions under which Russellian propositions in the sense of J. Barwise and J. Etchemendy [2] are paradoxical, and the computational complexity of the problems whether or not Russellian proposition is paradoxical, intrinsically paradoxical, and classical. 1
Propositional Logic
"... hat have been studied extensively. For example, "A is false", "A is true at time t" (from temporal Draft of August 31, 2000 6 Propositional Logic logic), "A is necessarily true " (from modal logic), "program M has type #"(from programming languages), etc. Re ..."
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Cited by 2 (0 self)
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hat have been studied extensively. For example, "A is false", "A is true at time t" (from temporal Draft of August 31, 2000 6 Propositional Logic logic), "A is necessarily true " (from modal logic), "program M has type #"(from programming languages), etc
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