PP-2009-06: The Great Art of Modeling

PP-2009-06: van Benthem, Johan (2009) The Great Art of Modeling. [Report]

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‘Possible worlds semantics’ for modal logic is a widely used term, sometimes with ominous metaphysical connotations, but what does this style of modeling involve today? We discuss three main issues, using epistemic logic as a running example, and drawing upon both mathematical results and practices in the expertise of working researchers. Our first question is a foundational one: how does one associate a type of model with a language, and what considerations affect that choice? Our focus is on invariance and definability results, familiar from the mathematical and computational tradition, though less so in philosophy. The second question is less deep, but maybe even more challenging in practice: once we have chosen a type of models for a language, how does one select and then maintain models appropriate to concrete scenarios of application? While there is a lot of ‘art’ to this in the literature, there is very little ‘science’ of model construction for modal logics. We show how this works in dynamic epistemic logics, and identify some current challenges for a true ‘modeling theory’ as opposed to the more abstract usual ‘model theory’. Finally, we discuss the pervasive tension between ‘thin’ and ‘thick’ worlds in modal logic, using examples from game theory, and pointing out how the contrast can be made fruitful.

Item Type: Report
Report Nr: PP-2009-06
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: model, philosophical logic, epistemic logic,dynamic logic
Subjects: Logic
Depositing User: Johan van Benthem
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/336

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