Recursive prime models for Boolean algebras

Prime Ideal Theorem for Double Boolean Algebras

Double Boolean algebras are algebras (D,u,t, , ,⊥,>) of type (2, 2, 1, 1, 0, 0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under u (resp. t). A filter F is called primary if F 6= ∅ and for all x ∈ D we have x ∈ F or x ∈ F . In this note we prove t...

Propagation Models and Fitting Them for the Boolean Random Sets

In order to study the relationship between random Boolean sets and some explanatory variables, this paper introduces a Propagation model. This model can be applied when corresponding Poisson process of the Boolean model is related to explanatory variables and the random grains are not affected by these variables. An approximation for the likelihood is used to find pseudo-maximum likelihood esti...

Algebras for Boolean Presuppositions

We present an algebraic approach to the semantics of presuppositions in dynamic semantics preconditions are introduced explicitly as separate components in the semantic algebra The approach is worked out for a propositional language that is interpreted in a Boolean setting We provide several meta mathematical results about the example some completeness issues are discussed and a decision method...

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...

Prime Higher Derivations on Algebras