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Traditional computational models of geographic phenomena offer no room for imperfection. Underlying this tradition is the simplifying assumption that reality is certain, crisp, unambiguous, independent of context, and capable of quantitative representation. This paper reports on initial work which explicitly recognises that most geographic information is intrinsically imperfect. Based on an ontology of imperfection the paper explores a formal model of imperfect geographic information using multi-valued logic. The development of Java software able to assist with a geodemographic retail site assessment application is used to illustrate the utility of a formal approach. Computer, Environment and Urban Systems v25 pp. 89-103. 2.1 Error, imprecision and vagueness Knowledge about reality is gained through observations. Observations are therefore first class objects in our account, rather than the underlying objects that are observed (Worboys, 1998a). Observations are imperfect in the sense that they can never fully or correctly reflect all aspects of reality. Imperfection is therefore the root of our ontology, as the concept refers generally to the inevitable deviations from perfection when observing reality. Imperfection can be thought of as comprising two distinct orthogonal concepts: error and imprecision. Error, or inaccuracy, concerns a lack of correlation of an observation with reality; imprecision concerns a lack of specificity in representation. Observations will usually be inaccurate and imprecise, but error and imprecision are orthogonal concepts since the level of accuracy of an observation is not implied by the level of precision, nor vice versa. Intuitively, the statement "York is in England" is at the same time more accurate and less precise than the statement "York is in Lancashire". The general definitions of accuracy and precision above correspond closely to the more specialised statistical definitions of the terms in common usage (see Drummond, 1995). Any observation of reality will be subject to imprecision: Veregin (1999) discusses some of the different causes and types of imprecision. Granularity is closely related, but not identical to imprecision. Granularity refers to the existence of clumps or grains in information, in the sense that individual elements in the grain cannot be distinguished or discerned apart. Granulation is therefore the result of distinct entities becoming indiscernible due to the imprecision in an observation. Observations or representations of coarser granularity offer less detail, for example where the clumping of information into pixels in remotely sensed images may prevent sub-pixel entities being distinguished (Fisher, 1997). Vagueness, however, is a special type of imprecision which concerns the existence of indeterminate borderline cases. "Yorkshire is in England" is not a vague statement (both Yorkshire and England have clearly defined national or international boundaries), but is an imprecise statement. Although intuitively more precise, "Yorkshire is in the East of ...

Information about dynamic spatial fields, such as temperature, windspeed, or the concentration of gas pollutant in the air, is important for many environmental applications. At the same time, the development of geosensor networks (wirelessly communicating, sensor-enabled small computing devices, distributed throughout a geographic environment) present new opportunities for monitoring of dynamic spatial fields in much more detail than ever before. This paper presents a new model for querying information about dynamic spatial fields using geosensor networks. In order to manage the inherent complexity of dynamic geographic phenomena, our approach in this paper is to focus on the qualitative representation of spatial entities, like regions, boundaries, and holes, and of events, like splitting, merging, appearance, and disappearance events. Based on combinatorial maps, we present a qualitative model as the underlying data management paradigm for geosensor networks that is capable of tracking salient changes in the network in a much more energy-efficient way. Further, our model enables reconfiguration of the communication in the geosensor network in response to changes in the environment. We present an algorithm capable of adapting sensor network granularity according to dynamic monitoring requirements. Regions of high variability can trigger increases in the geosensor network granularity, leading to more detailed information about the dynamic field. Conversely, regions of stability can trigger a coarsening of the sensor network, leading to efficiency increases in particular with respect to power consumption and longevity of the sensor nodes. Querying of this responsive geosensor network is also considered, and the paper concludes with a review of future research directions.

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