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Logic Journal of IGPL 1997 5(4):539-563; doi:10.1093/jigpal/5.4.539
© 1997 by Oxford University Press
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Compositional semantics for a language of imperfect information

W Hodges

School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1, UK. Email: W.Hodges@qmw.ac.uk

We describe a logic which is the same as first-order logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gives a compositional meaning to formulas of the 'information-friendly' language of Hintikka and Sandu. For first-order formulas the semantics reduces to Tarski's semantics for first-order logic. We prove that two formulas have the same interpretation in all structures if and only if replacing an occurrence of one by an occurrence of the other in a sentence never alters the truth-value of the sentence in any structure.

Keywords: game semantics, compositional, imperfect information, independence-friendly, branching quantifier, generalised quantifier, trump


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