On the Skeleton of Stonian p-Ortholattices

On the algebra of regular sets Properties of representable Stonian p-Ortholattices

The mereotopology RT− has in Stonian p-ortholattices its algebraic counterpart. We study representability of these lattices and show that not all Stonian p-ortholattices can be represented by the set of regular sets of a topological space. We identify five conditions that hold in algebras of regular sets and which can be used to eliminate non-representable Stonian p-ortholattices. This shows no...

Stonian p-ortholattices: A new approach to the mereotopology RT0

This paper gives a isomorphic representation of the subtheories RT−, RT− EC , and RT of Asher and Vieu’s first-order ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of p-ortholattices – lattices that are both orthocomplemented and pseudocomplemented – and show that the identity (x ·y)∗ = x∗+y∗ defines the...

A Note on Congruence Kernels in Ortholattices

We characterize ideals of ortholattices which are congruence kernels. We show that every congruence class determines a kernel.

On Matrices over the Ring of Continuous Complex Valued Functions on a Stonian Space

Formalization of Ortholattices via Orthoposets

There are two approaches to lattices used in the Mizar Mathematical Library: on the one hand, these structures are based on the set with two binary operations (with an equational characterization as in [17]). On the other hand, we may look at them as at relational structures (posets – see [12]). As the main result of this article we can state that the Mizar formalization enables us to use both ...