1 A BME View to the New Realities of TGIS.- 1.1 Introducing a Temporal Geographical Information System (TGIS).- 1.1.1 Purposefulness, Content, and Context.- 1.1.2 Synthesis, Organization, and Visualization.- 1.1.3 Action-Oriented.- 1.2 Field-Based TGIS.- 1.3 TGIS Functions.- 1.4 Novel Contribution to TGIS.- 1.4.1 BME-Based Advanced Functions.- 1.4.2 Stochastic Modelling.- 1.4.3 BMEIib Software.- 1.4.4 Epistemic Viewpoint.- 1.4.5 Scientific Hypothesis Testing and Explanation.- 1.4.6 Revisionistic Paradigm.- 1.5 Concluding Remarks.- 2 Spatiotemporal Modelling.- 2.1 Spatiotemporal Continuum.- 2.2 The Random Field Model.- 2.3 The Role of Metaphors in TGIS.- 2.4 The Importance of Physical Geometry.- 2.5 Synopsis.- 3 Knowledge Bases Integration.- 3.1 Integrating Knowledge Bases (KB) into TGIS.- 3.2 General KB and the Associated Physical Constraints.- 3.2.1 Space/Time Correlation Functions Between Two or More Points (Multiple-Point Statistics).- 3.2.2 Physical Models.- 3.3 Specificatory KB.- 3.3.1 Hard and Soft Data.- 3.3.2 The Effect of Soft Data on The Calculation of the Space/Time Correlation Functions.- 3.4 Accommodating Knowledge Needs.- 3.4.1 Knowledge Classification.- 3.4.2 Model Building and Reality Check.- 4 Spatiotemporal Mapping.- 4.1 A Formulation of the Spatiotemporal Mapping Problem.- 4.2 Formal BME Analysis and Mapping.- 4.2.1 The Basic BME Procedure.- 4.2.2 The Advantage of Composite Space/Time Mapping.- 4.2.3 Continuous-Valued Map Reconstruction.- 4.2.4 Modifications of the BME Procedure.- 4.2.5 Spatiotemporal Filtering.- 4.2.6 Spatiotemporal Mapping and Change-of-Scale Procedures.- 4.3 Other Mapping Techniques.- 4.3.1 Wiener-Kolmogorov Stochastic Interpolation.- 4.3.2 Geostatistical Kriging.- 4.3.3 Kalman-Bucy Filtering.- 4.3.4 Some Comparisons.- 4.4 Concluding Remarks.- 5 Interpretive BME.- 5.1 Interpretive Issues.- 5.2 An Epistemic Analysis of the BME Approach.- 5.3 Non-Bayesian Conditionalization.- 5.3.1 Material Biconditionalization.- 5.3.2 Material Cl(