Public Announcement Logic in HOL
This work provides a method for automating a specific logic in theorem proving, which is incremental as it builds on existing embedding techniques but addresses a previously unautomated logic.
The paper tackled the automation of public announcement logic with relativized common knowledge by presenting a shallow semantical embedding, enabling the first-time automation using off-the-shelf theorem provers for classical higher-order logic, as demonstrated through automated meta-theoretical studies and non-trivial reasoning tasks like the wise men puzzle.
A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. It is demonstrated (i) how meta-theoretical studies can be automated this way, and (ii) how non-trivial reasoning in the target logic (public announcement logic), required e.g. to obtain a convincing encoding and automation of the wise men puzzle, can be realized. Key to the presented semantical embedding -- in contrast, e.g., to related work on the semantical embedding of normal modal logics -- is that evaluation domains are modeled explicitly and treated as additional parameter in the encodings of the constituents of the embedded target logic, while they were previously implicitly shared between meta logic and target logic.