User:Magnap/Inquisitive Semantics Proposal: Difference between revisions

An important thing to bear in mind about inquisitive semantics is that it does not give us a Boolean algebra, but only a Heyting algebra, meaning that <math>\neg\neg\text{P} = \text{P}</math> is not guaranteed. In fact, the non-inquisitive projection operator <math>\lambda \text{P}. !\text{P}</math>, which collapses all the alternatives of a proposition into just one which contains them all, thus keeping the assertion the same but ensuring that no question is asked, ''is'' just <math>\lambda \text{P}. \neg\neg\text{P}</math>. Another important operator is the non-informative projection operator <math>\lambda \text{P}. ?\text{P} = \lambda \text{P}. \text{P} \lor \neg\text{P}</math>, which ensures that a proposition does assert anything by adding an alternative which covers all worlds that would otherwise have been ruled out.