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Partial Metrics, Fuzzy Equalities, and Metric-Entropy Pairs
Event Type: Colloquium Date: June 10, 2009 Time: 01:00PM - 02:30PM Venue: CC-2-2545 Abstract: Generalized metrics without the p(x,x)=0 axiom provide distances on the spaces of partially defined elements and, in particular, on the domains for denotational semantics.An especially popular variant of such distances involves adding axioms p(x,x) <= p(x,y) and p(y,y) + p(x,z) <= p(x,y) + p(y,z), resulting in the notion of partial metric. Equivalently, we can talk about weighted metrics and weighted quasi-metrics.
In a dual viewpoint, we can talk about Heyting-algebra-valued and quantale-valued fuzzy equalities. Quantale-valued fuzzy equalities and quantale-valued partial metrics coincide.
There are various connections between partial metrics and metric-entropy \wedge-pairs. The entropy \nu would typically give rise to a partial metric p(x,y) = \nu(x \wedge y), the metric part of the pair would then be the weighted metric assocated with p, and the conditional function of a \wedge-pair would be the weighted quasi-metric associated with p.
Speaker: Michael Bukatin Speaker Bio: Department of Computer ScienceBrandeis University
