Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

It's the premises that are a bit loopy. It's instructive and fun to see this in terms of formal logic, especially because the proof requires modal logic-- an extension of standard logic that ...

Modal logic is the study of the laws of inference for judgments ... This class will study the proof theory and meta theory of modal logics, and present the foundations for practical proof procedures.

This repository contains a recent formalization of a Henkin-style completeness proof for the strongest of the five systems of modal logic proposed by Lewis and Langford [2], namely, S5, using the Lean ...

Modal Reasoning: The study of logic that incorporates modalities—such as necessity, possibility, and knowledge—to characterise different states or conditions.

In this paper we present a modal extension of logic programming, which allows both multiple universal modal operators and embedded implications. We show that this extension is well suited for ...

For example, it becomes far simpler to formulate proof-systems for hybrid logic, and completeness results can be proved of a generality that is simply not available in modal logic. That is, ...