In [1] a description of a physical entity is given by means of a state property system and in [2] it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between classical properties and connectedness for closure spaces. The main result is a decomposition theorem, which allows us to split a state property system into a numb...

This paper describes a novel event-matching strategy using features obtained from the transitive closure of dependency relations. The method yields a model capable of matching events with an F-measure of 66.5%.

Let Λ be a signature and A = (A, Λ) be an algebra. We say that A is an algebra of binary relations if A ⊆ P(U × U) for some set U and each operation in Λ is interpreted as a natural operation on relations. 0 is the empty set. Other possible operations include reexive-transitive closure * , the residuals \ and / of composition, domain d and range r, etc. Algebras of binary relations Let Λ be a s...

In 1965 L. A Zadeh [11] introduced fuzzy sets as a generalization of ordinary sets. After that C. L. Chang [2] introduced fuzzy topology and that led to the discussion of various aspects of L-topology by many authors. The Čech closure spaces introduced by Čech E. [1] is a generalization of the topological spaces. The theory of fuzzy closure spaces has been established by Mashhour and Ghanim [4]...

It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices,...