The article surveys and evaluates various approaches to the logic of indeterminate situations. Two types of such situations are discussed: future contingents and quantum indeterminacy. Approaches differ according to whether they can salvage (i) classical tautologies (such as the law of excluded middle) as logical truths, (ii) bivalence and (iii) truth-functionality. What I call “the first solution” denies bivalence and either saves classical logical truths (supervaluations) or truth-functionality (multi-valued approach), but not both. The so-called “second solution”, saving all aforementioned features, harbors difficulties for the contingency of future contingents and is inapplicable in the quantum realm. Finally, the third solution saves bivalence but, at least in the case of quantum logic, abandons truth-functionality.
The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., \cite{pp:book,wata}). Recently an effort has been exercised to advance with logics that possess a symmetric difference (\cite{matODL,MP1}) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In \cite{matODL} the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result of this paper somewhat economizes on this construction: There is an ODL with 3 generators that is not set-representable (and so the free ODL with 3 generators cannot be set-representable). The result is based on a specific technique of embedding orthomodular lattices into ODLs. The ODLs with 2 generators are always set-representable as we show by characterizing the free ODL with 2 generators - this ODL is MO3×24.