A Reflective Proof System for Reasoning in Contexts

Pierre E. Bonzon

We consider the problem of building an automated proof system for reasoning in contexts. Towards that goal, we first define a language of contextual implications, and give its operational semantics under the form of a natural deduction system using explicit context assertions. We show that this proof system has an equivalent straightforward logic program, which in turn can be reified, i.e. defined as an outer meta-level context, and thus applied to itself. More powerful reasoning models (e.g. those involving theory lifting) can be then implemented by applying the same logic program on extended meta-level contexts containing specialized axioms. As a theoretical application, we consider the task of concept learning. In order to achieve generality (i.e. abstracting solution classes from problem instances), we argue that concept learning goals should aim at the discovery of meta-level operators representing the sequence of inference steps leading to object-level moves or actions. We illustrate this idea with the definition of a learning model based on partial deduction with respect to theory lifting.

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