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Positive fragments of relevance logic and algebras of binary relations

<11> This paper continues a major international research programme on relevance logic. We solve an open problem on completeness with respect to relational semantics, posed by M. Dunn ("Non-commutative linear logic", e-mail from 1992, available at www.seas.upenn.edu/~sweirich/types/archive/1992/msg00028), and R. Maddux ("Relevance logic and the calculus of relations" presented at International Conference on Order, Algebra and Logics, 2007, abstract available at www.math.vanderbilt.edu/~oal2007/submissions/submission_10.pdf). In particular, we show the incompleteness of the negation-free fragment of relevance logic.