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

dimensional Lie algebra over  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. 132-133]). A subspace W of G is called a Lie triple system in G if [X, [Y, Z

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

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 take-off; the take-off; the drive to maturity; the age of high mass consumption. Beyond the age

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

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 real-time systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via

geometry of oppositions, n-opposition, square of opposition, logical square, logical hexagon, logical bi-simplexes, logical poly-simplexes, contradiction, modal logic, concept, spatial logics, n-dimensional geometry, central symmetry, simplexes, Aristotelian p q-semantics, Aristotelian p q-lattice, 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.

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 non-truth-conditional understanding. And my tentativeness

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

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