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

Abstract

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.KeywordsDescription LogicType TheoryFirst Order LogicDependent TypeStop TimeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.