Using Three-Valued Logic to Specify and Verify Algorithms of Computational Geometry [chapter]

Jens Brandt, Klaus Schneider
2005 Lecture Notes in Computer Science  
Many safety-critical systems deal with geometric objects. Reasoning about the correctness of such systems is mandatory and requires the use of basic definitions of geometry for the specification of these systems. Despite the intuitive meaning of such definitions, their formalisation is not at all straightforward: In particular, degeneracies lead to situations where none of the Boolean truth values adequately defines a geometric primitive. Therefore, we use a three-valued logic for the
more » ... of geometric primitives to explicitly handle such degenerate cases. We have implemented a three-valued library of linear geometry in an interactive theorem prover for higher order logic which allows us to specify and verify entire algorithms of computational geometry.
doi:10.1007/11576280_28 fatcat:4se43sbd3rdghbtb7jt6xfppde