The logic induced by effect algebras.

Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras , we investigate a natural implication and prove that the implication reduct of is term equivalent to . Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras.

Operations and structures derived from non-associative MV-algebras.

The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g.