Extension properties of Boolean contact algebras

Prelegent(ci)

Ivo Duentsch

Afiliacja

Brock University, Kanada

Termin

12 kwietnia 2013 14:15

Pokój

p. 5820

Seminarium

Research Seminar of the Logic Group: Approximate reasoning in data mining

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Boolean contact algebras (BCAs) arise in spatial--temporal reasoning, and are hybrid algebraic--relational structures. Their history goes back to the 1920's, augmenting Leśniewski's mereology --whose models may be regarded as Boolean algebras with the least element removed -- with a binary predicate of ``being in contact''. A contact relation on a Boolean algebra B is, loosely speaking, a symmetric and reflexive relation C on the nonzero elements of B with additional compatibility properties. Standard models are Boolean algebras of regular closed sets of some topological space  X where two such sets are in contact if their intersection is not empty. Continuing last year's seminar, I will explore extension properties of BCAs: I will show that the class of Boolean contact algebras has the joint embedding property and the amalgamation property, and that the class of connected Boolean contact algebras has the joint embedding property but not the amalgamation property. By  Fraïssé's theorem, there is a unique countable homogeneous BCA. I will exhibit some properties of  this algebra and the relation algebra generated by its contact relation. It turns out that the algebra can be partitioned into four sets {0}, {1}, K, and L, which are the only orbits of the group of base automorphisms of the algebra, and that the contact relation algebra of this algebra is finite. This is the first non--trivial extensional BCA we know which has this property.

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