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 orthoalgebraic
framework. I will demonstrate that this formalism relates to a formal theory of
questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating
attitude questions, which normally are non-commuting, i.e., the ordering of the questions
affects the answer behavior of attitude questions. Further, it allows the expression
of conditional questions such as “If Mary reads the book, will she recommend it to
Peter?”, and thus gives the framework the semantic power of raising issues and being
informative at the same time. In the case of commuting observables, there are close
similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn
approach to question 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 orthoalgebraic approach is
able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore,
the general approach is suitable to describe the different types of (non-commutative)
attitude questions as investigated in modern survey research. Concluding, I will suggest
that an active dialogue between the traditional model-theoretic approaches to
semantics and the orthoalgebraic paradigm is mandatory.