Types for Proofs and Programs

Volume 1158 of the series Lecture Notes in Computer Science pp 165-182


A natural deduction approach to dynamic logic

  • Furio HonsellAffiliated withDipartimento di Matematica e Informatica, Università di Udine
  • , Marino MiculanAffiliated withDipartimento di Matematica e Informatica, Università di UdineDipartimento di Informatica, Università di Pisa

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Natural Deduction style presentations of program logics are useful in view of the implementation of such logics in interactive proof development environments, based on type theory, such as LEGO, Coq, etc. In fact, ND-style systems are the kind of systems which can take best advantage of the possibility of reasoning “under assumptions” offered by proof assistants generated by Logical Frameworks. In this paper we introduce and discuss sound and complete proof systems in Natural Deduction style for representing various “truth” consequence relations of Dynamic Logic. We discuss the design decisions which lead to adequate encodings of these logics in Coq. We derive in Dynamic Logic a set of rules representing a ND-style system for Hoare Logic.