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

Authors:
Davide Bresolin;Valentin Goranko;Angelo Montanari;Pietro Sala
Affiliations:
Department of Computer Science, University of Verona, Verona, Italy;School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Department of Mathematics and Computer Science, University of Udine, Udine, Italy;Department of Mathematics and Computer Science, University of Udine, Udine, Italy
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

We introduce special pseudo-models for the interval logic of proper subintervals over dense 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 terminating tableau for that logic. The case of proper subintervals is essentially more complicated than the case of strict subintervals, for which we developed a similar tableau-based decision procedure in a recent work.