ISA Project

Indoor Spatial Theory

Principle Investigator Dr. Mike Worboys.

This online summary and related material are working drafts for the ISA Project. The material summarized below is excerpted from

• Walton, L. and M. Worboys (2009). An Algebraic Approach to Image Schemas for Geographic Space . International Conference on Spatial Information Theory (COSIT 2009), Aber Wrac'h, France. (Submitted).

See our publications and reports for further project results and publications.

Image Schemas for Indoor Space

Milner (2009) argues that models for spatially-rich systems should provide visualization tools that are tightly coupled with a formal system in order to support the needs of diverse communities including end-users, programmers, system designers, and theoretical analysts. Milner's bigraphical models (bigraphs) provide a formal method for independently specifying mobile connectivity and mobile locality, providing a unified platform for designing, formally modeling, analyzing, and visualizing ubiquitous systems. Bigraphs were developed for the virtual world of communicating processes and ambient information objects. While it has been argued that agents can be physical and can influence informatics domains, it has not yet been demonstrated that bigraphs are suitable models for mixed virtual and physical environments.

Image schemas (Johnson 1987), used to embody spatiotemporal experiential abstractions, model conceptual patterns that can be physical or non-physical. Schemas have long been used to model key spatio-temporal concepts in geographic spaces, such as the notion that spaces and objects can serve as CONTAINTERs for other spaces or objects and that objects can follow PATHs through space and time. While it has been argued that image schemas provide appropriate patterns for representing object properties, relations, and behaviors, there has not been any generally accepted formal mathematical model for image schemas.

We argue that image schemas can be formailized in bigraphs, and that together they provide a useful strategy for modeling indoor spaces and spatial object properties, relations, and behaviors. For example, the bigraph in the figure below shows an indoor scene with triangular nodes for agents (A), square nodes for computers (C), and elliptical nodes for rooms (R), and buildings (B). All nodes can be connected to other nodes by edges so that any agent can simultaneously be on the phone and on a computer and any computer can simultaneously connect to an agent and network in a building.

Agent A1 and computer C1 are inside room R1 in building B1. Another agent (A2) is inside a second room (R2), and a third agent (A3) is elsewhere. Each of these relations is an example of the image schema CONTAINER, which is modeled in a bigraph by allowing nodes to be placed inside other nodes. Three agents (A1, A2, A3) participate in a conference call (e1), edge e2 indicates that the first agent (A1) is on a computer (C1), and edge e3 shows that the computer (C1) is connected to a LAN in the building (B1). These connectivity relations are examples of the image schema LINK, which is visually shown in a bigraph by allowing nodes to link to one or many other nodes. This example is based on a built environment example defined by Milner which we have interpreted in terms of image schemas.

In the full paper we provide a method for formally representing, visualizing, and reasoning about topological and physical image schemas for indoor spaces. Our primary goal is to demonstrate that bigraphical models are appropriate formalization and visualization tools for representing static and dynamic image schemas in indoor spaces. Our examples take a subset of existing image schemas (e.g. CONTAINER, LINK, and BLOCKAGE) and use them to model various indoor scenes, scene sequences, and scene compositions using bigraphs.

References:

• Johnson, M. (1987). The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason. University Of Chicago Press.
• Milner, R.(2009). The Space and Motion of Communicating Agents. Cambridge University Press. Forthcoming.