A Logic of Vision

Michiel van Lambalgen, Jaap van der Does

This essay is on logical aspects of uncertain, unstable perceptual information. The main idea is to develop a logic based on Marr's cognitive theory of vision (Marr 1982).

In Marr's theory, vision is a multi-layered process. The different layers have filters of different gradation, which makes vision at each of them approximate. Indeed, our main tasks were:

The first task is formalised by means of an inverse systems of first order models, with reality appearing as its inverse limit. The second task is formalised by means of conditional quantifiers, a form of generalised quantification. We show that the logic provides for a semantics and pragmatics of direct perception reports. In particular, direct perception reports have a possibly nonveridical, approximative semantics, which becomes veridical by our pragmatic expectation that what is perceived will remain the case.

The logic of vision is resource bounded, where the resources consist of frames over sets of assignments. Conditional quantifiers use such frames to filter the information given by a formula. This kind of filtering has interesting logical characteristics in common with the blurring of reality that figures in describing perception.

It is a general feature of resource bounded logics that the underlying logics are weak, but that stronger principles can be obtained pragmatically, by strengthening the resource. For the logic of vision this feature is clarified by showing how changes in the resource capture different notions of partiality, and by studying how the perception verb interacts with connectives and quantifiers in different visual contexts. The inference Veridicality, which does not hold generally, is also studied in depth.

We end by arguing that the logic of vision formalises Husserl's philosophy of perception. It also suggests a semantics for some evidentials.

See also the information on Jaap's homepage.

Last modified: Thursday, 02-Jan-2003 17:03:20 CET

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