Looking at Separation Algebras with Boolean BI-eyes

In this paper, we show that the formulae of Boolean BI cannot distinguish between some of the different notions of separation algebra found in the literature: partial commutative monoids, either cancellative or not, with a single unit or not, all define the same notion of validity. We obtain this result by the careful study of the specific properties of the counter-models that are generated by tableaux proof-search in Boolean BI.

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