Project Report Categorical Judgments in a Logical Framework 15-816 Modal Logic

Categorical judgments possess a context-clearing property, making them difficult to express elegantly in the LF logical framework because the context of available LF hypotheses grows monotonically. We describe a connection between categorical judgments and a refinement to open terms of LF’s subordination relation. Leveraging this connection, we propose a logical framework, based on open-terms subordination, that supports elegant higher-order encodings of categorical judgments. As a concrete example of its expressive power, we present an encoding of judgmental S4 modal logic and establish its adequacy.