Dual tableau for a multimodal logic for order of magnitude qualitative reasoning with bidirectional negligibility

We present a relational proof system in the style of dual tableaux for the relational logic associated with a multimodal propositional logic for order of magnitude qualitative reasoning with a bidirectional relation of negligibility. We study soundness and completeness of the proof system and we show how it can be used for verification of validity of formulas of the logic.