On extending of partial Boolean algebras to partial *-algebras

Extending partial combinatory algebras

Extending partial combinatory algebras

We give a negative answer to the question whether every partial combinatory algebra can be completed. The explicit counterexample will be an intricately constructed term model, the construction and the proof that it works heavily depending on syntactic techniques. In particular, it is a nice example of reasoning with elementary diagrams and descendants. We also include a domain-theoretic proof ...

Partial * - algebras of Distributions

The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of C∞-vectors of a self-adjoint operator, is considered in the framework of the so-called duality method. The multiplication is defined by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain...

Pseudo-BCK algebras as partial algebras

It is well-known that the representation of several classes of residuated lattices involves lattice-ordered groups. An often applicable method to determine the representing group (or groups) from a residuated lattice is based on partial algebras: the monoidal operation is restricted to those pairs which fulfil a certain extremality condition, and else left undefined. The subsequent construction...

Partial Boolean Algebras as Models for Thesaurus Integration

A model of a collection of documents based on partial Boolean algebras is presented. This model has been considered while analysing a problem of integration of thesauri. Some properties of partial Boolean algebras are exploited in defining theoretical tools for information retrieval associated to this model. Such tools are a logical language representing queries to the system and a browsing mec...