Symbolic expressions within a spatial algebra: unification and impact upon spatial reasoning

Spatial reasoning in symbolic images requires a means for identification of spatial relationships. In earlier work (see E. Jungert and S.-K. Chung, Proc. IFIP TC-2 Working Conf. on Visual Database Systems, Tokyo, Japan, 1989) an algebra based on symbolic projections for manipulation and transformation of symbolic images has been defined. Although that symbolic algebra was quite powerful for manipulation of symbolic images, it did not include any means for spatial reasoning. With such a goal it was already clear at an early stage that the algebra had to be developed further. A description is given of the unification of algebraic expressions, which offers a powerful basis for spatial reasoning. It is shown that the algebra constitutes a basis for a tool for spatial reasoning in symbolic images