Journal of Logic, Language and Information

, Volume 21, Issue 3, pp 237–277 | Cite as

Questions and Answers in an Orthoalgebraic Approach

  • Reinhard BlutnerEmail author
Open Access


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.


Attitude questions Commutativity Conditional questions Decorated partitions Orthoalgebra Orthodox quantum theory Qubit Question semantics Structured propositions Survey research 



Thanks for valuable comments and discussions go to Maria Aloni, Anton Benz, Stefan Blutner, Hans-Martin Gärtner, Peter beim Graben, Manfred Krifka, Michiel van Lambalgen, Salvador Mascarenhas, Emar Maier, Floris Roelofsen, and two anonymous referees of JoLLI. Further, I thank the participants of an ESSLLI (2011) class on geometric models of meaning (see, my students on quantum probabilities in Amsterdam (see, and the participants of my lectures on ortho-algebraic semantics held at ZAS in 2008. Special thanks go to Anton Benz and Hans-Martin Gärtner for initiating the ZAS lectures.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute for Logic, Language, and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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