Reasoning about Relations with Dependent Types: Application to Context-Aware Applications

Generally, ontological relations are modeled using fragments of first; order logic (FOL) and difficulties arise when meta-reasoning is done over ontological properties, leading to reason outside the logic. Moreover, when such systems are used to reason about knowledge and meta-knowledge, classical languages are not able to cope with different levels of abstraction in a clear and simple way. In order to address these problems, we suggest a formal framework using a dependent (higher order) type theory. It maximizes the expressiveness while preserving decidability of type checking and results in a coherent theory. Two examples of meta-reasoning with transitivity and distributivity and a case study illustrate this approach.