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Johan van Benthem

The Art of Modeling


ISBN: 978-3-88405-506-9

Price: €7.50 (including 19 % tax)


Abstract to Contribution

Johan van Benthem  makes modal semantics his main topic. He discusses three main issues, using in all of them the case of epistemic logic as a continuing example. The first concerns the question: How does one associate a type of model with a language, and what considerations affect this choice? In discussion, van Benthem focuses on some results concerning modal bisimulation invariance and definability results. He insists that we should take the internal relations between worlds inside one modal model very seriously. The second question deals with the selection of models appropriate to concrete scenarios of application. Van Benthem suggests that there is a lot of “art” but very little “science” in the construction of models for modal logic. He proposes that there is a systematic “modeling theory” behind current best practices in the art of logical modeling, which deserves further study and perhaps inclusion in the standard logic curriculum. He additionally makes a general important point about possible world models: that we should take external relations seriously, as holding between wholes and possible worlds models. The third and last topic of the paper is the tension van Benthem perceives between “thin” and “thick” conceptions of worlds in modal logic, both of which have been widely used. He proposes a concrete result concerning how transformations on thin models can be retrieved in a thick setting, concluding that: “once thin and thick models are brought together in this precise manner, ideas can flow in both directions.”

Authors Biography

Johan van Benthem here  makes modal semantics his main topic. He discusses three main issues, using in all of them the case of epistemic logic as a continuing example. The first concerns the question: How does one associate a type of model with a language, and what considerations affect this choice? In discussion, van Benthem focuses on some results concerning modal bisimulation invariance and definability results. He insists that we should take the internal relations between worlds inside one modal model very seriously. The second question deals with the selection of models appropriate to concrete scenarios of application. Van Benthem suggests that there is a lot of “art” but very little “science” in the construction of models for modal logic. He proposes that there is a systematic “modeling theory” behind current best practices in the art of logical modeling, which deserves further study and perhaps inclusion in the standard logic curriculum. He additionally makes a general important point about possible world models: that we should take external relations seriously, as holding between wholes and possible worlds models. The third and last topic of the paper is the tension van Benthem perceives between “thin” and “thick” conceptions of worlds in modal logic, both of which have been widely used. He proposes a concrete result concerning how transformations on thin models can be retrieved in a thick setting, concluding that: “once thin and thick models are brought together in this precise manner, ideas can flow in both directions.”



 





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