Questions and Answers in an Orthoalgebraic Approach
Reinhard Blutner
Abstract:
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.