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A Dual Tableau-based Decision Procedure for a Relational Logic with the Universal Relation (Extended Version)
We present a first result towards the use of entailment in- side relational
dual tableau-based decision procedures. To this end, we introduce a fragment of
RL(1) which admits a restricted form of composition, (R ; S) or (R ; 1), where
the left subterm R of (R ; S) is only allowed to be either the constant 1, or a
Boolean term neither containing the complement operator nor the constant 1,
while in the case of (R ; 1), R can only be a Boolean term involving relational
variables and the operators of intersection and of union. We prove the
decidability of the fragment by defining a dual tableau- based decision
procedure with a suitable blocking mechanism and where the rules to decompose
compositional formulae are modified so to deal with the constant 1 while
preserving termination. The fragment properly includes the logics presented in
previous work and, therefore, it allows one to express, among others, the
multi-modal logic K with union and intersection of accessibility relations, and
the description logic ALC with union and intersection of roles.Comment: Extended version of the conference paper: D. Cantone, M.
Nicolosi-Asmundo, E. Or{\l}owska. A Dual Tableau-based Decision Procedure for
a Relational Logic with the Universal Relation. In Proceedings of the 29th
Italian Conference on Computational Logic, Torino, Italy, June 16-18, 2014.
CEUR Workshop Proceedings Vol. 1195, pp. 194-209 (2014