, Volume 192, Issue 3, pp 535–562 | Cite as

Agnostic hyperintensional semantics

  • Carl PollardEmail author


A hyperintensional semantics for natural language is proposed which is agnostic about the question of whether propositions are sets of worlds or worlds are (maximal consistent) sets of propositions. Montague’s theory of intensional senses is replaced by a weaker theory, written in standard classical higher-order logic, of fine-grained senses which are in a many-to-one correspondence with intensions; Montague’s theory can then be recovered from the proposed theory by identifying the type of propositions with the type of sets of worlds and adding an axiom to the effect that each world is the set of propositions which are true there. Senses are compositionally assigned to linguistic expressions by a categorial grammar with only two rule schemas, based on the implicative fragment of intuitionistic linear propositional logic, and a fully explicit grammar fragment is provided that illustrates the compositional assignment of sense to a variety of constructions, including dummy-subject constructions, infinitive complements, predicative adjectives and nominals, raising to subject, ‘tough-movement’, and quantifier scope ambiguities. Notably, the grammar and the derivations that it licenses never make reference to either worlds or to the extensions of senses.


Hyperintension Proposition World Higher order logic Linear logic Categorial grammar 



AHS is the result of joint work with Andy Plummer. The dynamic extension of the theory arises from a collaboration with Scott Martin. For corrections and helpful comments on an earlier version, thanks are due to Manjuan Duan, Murat Yasavul, and an anonymous referee.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.The Ohio State UniversityColumbusUSA

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