Questions and Answers in an Orthoalgebraic Approach

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.
Keywords Attitude questions  Commutativity  Conditional questions  Decorated partitions  Orthoalgebra  Orthodox quantum theory  Qubit  Question semantics  Structured propositions  Survey research
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References found in this work BETA
Charles L. Hamblin (1973). Questions in Montague English. Foundations of Language 10 (1):41-53.
J. Isaacs & K. Rawlins (2008). Conditional Questions. Journal of Semantics 25 (3):269-319.
Lauri Karttunen (1977). Syntax and Semantics of Questions. Linguistics and Philosophy 1 (1):3--44.

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