In a series of recent articles Angelika Kratzer has argued that the standard account of modality along Kripkean lines is inadequate in order to represent context-dependent modals. In particular she argued that the standard account is unable to deliver a non-trivial account of modality capable of overcoming inconsistencies of the underlying conversational background. She also emphasized the difficulties of characterizing context-dependent conditionals. As a response to these inadequacies she offered a two-dimensional account of contextual modals. Two conversational backgrounds are essentially used in this characterization of contextual modality.
We show in this paper that Kratzer’s double relative models (with finite domains) are elementary equivalent to well known neighborhood models of normal modalities originally proposed by D. Scott [S] and R. Montague [M]. We also argue that neighborhood models can be also used to represent some (non-normal) graded modalities that are difficult to represent in her framework (like ‘it is likely that’ or ‘it is highly probable that’, etc). Finally we show that an extension of the neighborhood semantics of conditionals is able to capture some of her proposals concerning dyadic modals. DR models with infinite domains can be shown to be pointwise equivalent to neighborhood models, but they are not guaranteed to have relational counterparts. So DR models surpass the representational power of relational (Kripkean) models. Neighborhood representations are, nevertheless, always possible, making clear as well that the central feature of double relative modals is that they are capable of encoding two central aspects of context: its propositional content, and its dynamic properties (which in Kratzer’s models are represented via an ordering source).
KeywordsModal Logic Minimal Model Modal Base Standard Account Contextual Modal
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