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Fuzzy logic with evaluated syntax for sound geometric reasoning with geographic information

Many approaches to fuzzifying classical geometries have been proposed and elaborated in the literature. From the field of geographic information science arises the need for yet another approach to the problem, which requires the generalization of ideal points and lines as two-dimensional possibilistic location constraints. We show that geometric reasoning with these location constraints does not satisfy the classical axioms of geometry. As a consequence, geometric reasoning in geographic information systems is not sound and often produces erroneous output. An error propagation calculus for possibilistic location constraints is needed. The paper proposes a framework for defining such an error calculus based on an axiomatic approach to geometric reasoning using fuzzy logic with evaluated syntax as a similarity logic.