Considering the inference rules in generalized logics, J.C. Abbott arrives to the notion of orthoimplication algebra (see Abbott (1970) and Abbott (Stud. Logica. 2:173-177, XXXV)). We show that when one enriches the Abbott orthoimplication algebra with a falsity symbol and a natural -type operation, one obtains an orthomodular difference lattice as an enriched quantum logic (see Matoušek (Algebra Univers. 60:185-215, 2009)). Moreover, we find that these two structures endowed with the natural morphisms are categorically equivalent. We also show how one can introduce the notion of a state in the Abbott algebras strenghtening thus the relevance of these algebras to quantum theories.

The Suppes-Zanotti inequalities involving the joint expectations of just three binary quantum observables are (re-)derived by the hull computation of the respective correlation polytope. A min-max calculation reveals its maximal quantum violations correspond to a generalized Tsirelson bound. Notions of "contextuality" motivated by such violations are critically reviewed.

In the QBist approach to quantum mechanics, a measurement is an action an agent takes on the world external to herself. A measurement device is an extension of the agent and both measurement outcomes and their probabilities are personal to the agent. According to QBism, nothing in the quantum formalism implies that the quantum state assignments of two agents or their respective measurement outcomes need to be mutually consistent. Recently, Khrennikov has claimed that QBism's personalist theory of quantum measurement is invalidated by Ozawa's so-called intersubjectivity theorem. Here, following Stacey, we refute Khrennikov's claim by showing that it is not Ozawa's mathematical theorem but an additional assumption made by Khrennikov that QBism is incompatible with. We then address the question of intersubjective agreement in QBism more generally. Even though there is never a necessity for two agents to agree on their respective measurement outcomes, a QBist agent can strive to create conditions under which she would expect another agent's reported measurement outcome to agree with hers. It turns out that the assumptions of Ozawa's theorem provide an example for just such a condition.