I think in general whats probably going on is that we have a couple of very large fields of study nonclassical logic and the interpretation of quantum mechanics that have been studied for generations attacked from many different angles and discussed within a variety of foundational frameworks The article seems to be describing one very specific approach within a much larger field of quantum logic and nonclassical logic The difficulties this raises are I think that  the article doesnt acknowledge its narrow focus and  because of its narrow focus the article makes foundational assumptions that will not be understood by people who arent acquainted with the particular specific approach it describes Eg I have a PhD in physics and have a general acquaintaince with nonclassical logic from reading the book by Priest but the hidden assumptions behind some of the articles casual use of terminology arent at all clear to me I cant tell whether its assuming the law of the excluded middle I cant tell whether it assumes truthvalue gluts I cant tell whether the definition of ptrue as  is meant to imply the definition of pfalse as  or as  In the lead we have On the other hand the propositions p and q and p and r are both false since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle Now the premise stated in the second clause of this sentence is literally incorrect although you claim that its correct in spirit but I think the conclusion stated in the first clause is also another example of the lack of appropriate attention to foundational issues I think its true that there is no wavefunction for which  On the other hand there are many wavefunctions for which  is greater than  and less than  There may be some specific foundational framework this leads to p and qfalse but the article doesnt spell out what that framework is and doesnt show an awareness that the choice of such a framework is a nontrivial one