By Kripke Saul
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Additional info for A Completeness Theorem in Modal Logic (paper)
Categorial Grammar Johan van Benthem’s work on categorial grammar [30, 41, 43] is in line with the above-mentioned dynamic view of language. In Categorial Grammar, a grammatical category is identified with a function type A ! B, taking arguments of type A into values of type B. This is an inherently procedural view: linguistic expressions denote procedures that change a state of some given type into a state of another type. The procedures corresponding to compound expressions are computed by deriving corresponding sequents in some appropriate categorial logic.
To use van Benthem’s famous slogan, ‘‘natural language is a programming language for cognition’’. But moreover, most l On the Trails of Logical Dynamics of van Benthem’s work on the syntax, semantics and pragmatics of Natural Language is ‘‘dynamic’’ in spirit, being in fact closely connected to his research on logical dynamics. Indeed, the original version of the above-mentioned quote is more precise in this sense: ‘‘Natural language is a programming language for effecting cognitive transitions between information states and its users’’ .
Logical games versus the logic of games. The first important distinction made by van Benthem is between on the one hand the view of ‘‘logic as games’’, view embodied in a multitude of logical games, and on the other hand the logic of games, approach that manifests itself in a variety of logics for reasoning about games. While the first is a game-theoretic approach to logic, the second provides a logic-based perspective on games. Games in Logic. g. g. the bisimilarity game) and model-building games etc.
A Completeness Theorem in Modal Logic (paper) by Kripke Saul