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Interactive Theorem Proving for Logic and Information

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Natural Language Processing in Artificial Intelligence — NLPinAI 2021

Part of the book series: Studies in Computational Intelligence ((SCI,volume 999))

Abstract

Automated reasoning is the study of computer programs that can build proofs of theorems in a logic. Such programs can be either automatic theorem provers or interactive theorem provers. The latter are also called proof assistants because the user constructs the proofs with the help of the system. We focus on the Isabelle proof assistant. The system ensures that the proofs are correct, in contrast to pen-and-paper proofs which must be checked manually. We present applications to logical systems and models of information, in particular selected modal logics extending classical propositional logic. Epistemic logic allows intelligent systems to reason about the knowledge of agents. Public announcements can change the knowledge of the system and its agents. In order to account for this, epistemic logic can be extended to public announcement logic. An axiomatic system consists of axioms and rules of inference for deriving statements in a logic. Sound systems can only derive valid statements and complete systems can derive all valid statements. We describe formalizations of sound and complete axiomatic systems for epistemic logic and public announcement logic, thereby strengthening the foundations of automated reasoning for logic and information.

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Acknowledgement

We thank Frederik Krogsdal Jacobsen for comments on drafts.

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Authors and Affiliations

  1. Technical University of Denmark, Kongens Lyngby, Denmark

    Jørgen Villadsen, Asta Halkjær From & Alexander Birch Jensen

  2. Aalborg University Copenhagen, Copenhagen, Denmark

    Anders Schlichtkrull

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  1. Department of Algebra and Logic, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Roussanka Loukanova

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Villadsen, J., From, A.H., Jensen, A.B., Schlichtkrull, A. (2022). Interactive Theorem Proving for Logic and Information. In: Loukanova, R. (eds) Natural Language Processing in Artificial Intelligence — NLPinAI 2021. Studies in Computational Intelligence, vol 999. Springer, Cham. https://doi.org/10.1007/978-3-030-90138-7_2

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