We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

The formal definition of abduction asks what needs to be added to a knowledge base to enable an observation to be entailed. TBox abduction in description logics (DLs) asks what TBox axioms need to be added to a DL knowledge base to allow a TBox axiom to be entailed. We describe a sound and complete algorithm, based on the standard DL tableau, that takes a TBox abduction problem in ALC and gener...

•radically change the economics of building large knowledge bases •provide a platform for cognitive simulations of larger-scale phenomena •Learning Reader learns by reading simplified language texts •Manages syntactic complexity •Unconstrained vocabulary, unlike controlled languages •Learning Reader combines •Natural language processing •A large-scale knowledge base •Deductive reasoning •Analog...

The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on ri...

Strongly Unfoldable Cardinals Made Indestructible by Thomas A. Johnstone Advisor: Joel David Hamkins I provide indestructibility results for weakly compact, indescribable and strongly unfoldable cardinals. In order to make these large cardinals indestructible, I assume the existence of a strongly unfoldable cardinal κ, which is a hypothesis consistent with V = L. The main result shows that any ...

This paper contributes to the literature of pro-poor growth measurement by introducing a growth-rate consistency axiom. The axiom states that if one growth pattern is judged to be more pro-poor than another growth pattern at a given growth rate, then the pro-poor ranking between the two growth patterns should remain the same at a higher growth rate. We show that summary pro-poor measures such a...

Dealing with uncertainty is a very important issue in description logics (DLs). In this paper, we present PrDL‐ Litebool N a new probabilistic extension of DL‐ Litebool N by supporting the belief interval in a single axiom or a set of axioms connected with conjunction (by ∧ ) or disjunction (by ∨ ) operators. The PrDL‐ Litebool N semantics is based on DL‐ Litebool N features which are a new alt...