Abstract
Dov Gabbay is not just a 50-year-old person, his name also denotes a phenomenon. I have felt his and its influence for many years: which are hereby gratefully acknowledged. Two of these influences are especially relevant for what follows. The first is Dov’s general view of modal logic as a theory of first-order definable operators over relational models (Gabbay [8]). The second is his work on labelled deduction as a general format for the proof theory of substructural logics with a resource-sensitive slant, be it categorial or dynamic (Gabbay [9]). This generalizes standard type theories, with their binary statements assigning types to terms, or proofs to propositions. The two themes are related. In my view, the following equation sums up much of Dov’s recent work.
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Van Benthem, J. (1999). Proofs, Labels and Dynamics in Natural Language. In: Ohlbach, H.J., Reyle, U. (eds) Logic, Language and Reasoning. Trends in Logic, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4574-9_3
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