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The Focused Constraint Inverse Method for Intuitionistic Modal Logics

Summary: The Focused Constraint Inverse Method for
Intuitionistic Modal Logics
Sean McLaughlin and Frank Pfenning
Carnegie Mellon University
Abstract. We present a focused inverse method for proof search in a variety of
intuitionistic modal logics such as K, D, T, S4 and S5. Unification of world-
paths for such logics is non-unitary and therefore handled by adding constraints
to sequents. We sketch proofs of soundness and completeness with respect to in-
tuitionistic modal natural deduction and describe our implementation. Potential
applications lie in multi-modal intuitionistic logics that have recently been pro-
posed to reason about authorization and information flow security.
1 Introduction
Intuitionistic modal logics (IMLs) are extensions of intuitionistic logic that incorpo-
rate modalities for reasoning about judgments other than categorical truth. There are
numerous applications of IMLs. They can, for instance, be used to reason about dis-
tributed computing environments where the modalities express which resources, such
as data and processors, are accessible from which other resources [25]. IMLs are used
to reason about authentication and security policies [10, 8]. For example, they can for-
malize questions such as: "Given a policy and Alice's current permissions, does she
have permission to open Bob's file?".


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University
Pfenning, Frank - School of Computer Science, Carnegie Mellon University


Collections: Computer Technologies and Information Sciences; Mathematics