Complete and Terminating Tableau for the Logic of Proper Subinterval Structures Over Dense Orderings

We introduce special pseudo-models for the interval logic of propersubintervalsoverdense linear orderings. We prove finite model property with respect to such pseudo-models, and using that result we develop a decision procedure based on a sound, complete, and terminatingtableau for that logic. The case of propersubintervals is essentially more complicated than the case of strict subintervals, for which we developed a similar tableau-based decision procedure in a recent work.