On Wed, Apr 23, 2014 at 4:08 PM, martin <martin@ics.forth.gr> wrote:

We adopted Allen's temporal logic, probably prematurely, thinking we could rely on
a well received theory. In the meanwhile, it turns out that Allen's logic does not work
properly both for fuzzy dates and for incomplete knowledge. There are temporal relations
which come from observation, but can only be represented by OR combinations of Allen's
relationships. That causes problems in RDF - we need superproperties of Allen's to represent
an OR. The other problem is that equality in time can only come from numerical declaration
of a date, but not from observation, except if the event is identical.

Pat Hayes's  catalog of temporal theories may help clarify things. Section 4.1 et. seq. are particularly relevant, but it's better to read the whole thing.    

Hayes, PJ (1996) A Catalog of Temporal Theories. Technical Report UIUC-BI-AI-96-01, University of Illinois.

Some axiomatizations have been further refined  by Gruninger and Ong - see e.g. http://stl.mie.utoronto.ca/publications/colore-time.pdf

See the colore ontology repository at https://code.google.com/p/colore/