This paper outlines the reductive modularization and verification of the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE). The ontology makes distinctions between enduring and perduring entities which is reflected in the resulting reductive modules, in contrast to previous work done to generate a consistency proof for DOLCE. We present our approach to verify DOLCE with math...

The aim of this paper is to identify a certain tensor category of perverse sheaves on the real loop Grassmannian GrR of a real form GR of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a reductive complex algebraic subgroup H of the dual group Ǧ. The root system of H is closely related to the restricted root system of GR. The fact that...

The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left k-step reductive Ω-algebras, and of right n-step reductive Ω-algebras, are indep...

We study homogeneous Lorentzian manifolds M=G/L of a connected reductive Lie group G modulo subgroup L, under the assumption that M is (almost) G-effective and isotropy representation totally reducible. show description such reduces to case semisimple groups G. Moreover, we prove space reductive. describe all reducible subgroups Lorentz divide them into three types. The Type I are compact, whil...