Questions and Answers in an Orthoalgebraic Approach

Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the ortho-algebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows to formulate conditioned questions such as “if electron 1 has spin ↑ what is the spin of electron 2?”, and thus gives it the semantic power of inquisitive semantics. In the case of commuting observables, there are close similarities between the ortho-algebraic approach to questions and the Jäger/Hulstijn approach to inquisitive semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the ortho-algebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. It will be shown that the present decorated partition theory is fully compatible with the structured meaning approach to questions assuming the latter can be extended to include conditioned questions. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the ortho-algebraic paradigm is mandatory.