In relation to semantics, “grounding” has two relevant meanings. “Symbol grounding” is the process of connecting symbols to perception and the world. “Communicative grounding” is the process of interactively adding to common ground in dialog. Strategies for grounding in human communication include, crucially, strategies for resolving troubles caused by various kinds of miscommunication. As it happens, these two processes of grounding are closely related. As a side-effect of grounding an utterance, dialog participants may adjust the meanings they assign to linguistic (...) expressions, in a process of semantic coordination. Meanings of at least some expressions include perceptual aspects which enable DPs to classify entities as falling under the expression or not based on their perception of those entities. We show how perceptual grounding of symbols can be achieved in a process of interactively adding to common ground. This requires that perceptual aspects of meaning can be updated as a result of participating in linguistic interaction, thereby enabling fine-grained semantic coordination of perceptually grounded linguistic meanings. A formal semantics for low-level perceptual aspects of meaning is presented, tying these together with the logical-inferential aspects of meaning traditionally studied in formal semantics. The key idea is to model perceptual meanings as classifiers of perceptual input. This requires a framework where intensions are represented independently of extensions, and structured objects which can be modified as a result of learning. We use Type Theory with Records, a formal semantics framework which starts from the idea that information and meaning are founded on our ability to perceive and classify the world, that is, to perceive objects and situations as being of types. As an example of our approach, we show how a simple classifier of spatial information based on the Perceptron can be cast in TTR. (shrink)