Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Isar - A Generic Interpretative Approach to Readable Formal Proof Documents
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
System Description: Proof Planning in Higher-Order Logic with Lambda-Clam
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A Refinement of de Bruijn's Formal Language of Mathematics
Journal of Logic, Language and Information
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
The Seventeen Provers of the World: Foreword by Dana S. Scott (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence)
System for Automated Deduction (SAD): A Tool for Proof Verification
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Computer assisted reasoning with MIZAR
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
IBM Journal of Research and Development
A Review of Mathematical Knowledge Management
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Evidence algorithm and system for automated deduction: a retrospective view
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
A User-friendly Interface for a Lightweight Verification System
Electronic Notes in Theoretical Computer Science (ENTCS)
Cybernetics and Systems Analysis
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Formalizing mathematical argument is a fascinating activity in itself and (we hope!) also bears important practical applications. While traditional proof theory investigates deducibility of an individual statement from a collection of premises, a mathematical proof, with its structure and continuity, can hardly be presented as a single sequent or a set of logical formulas. What is called "mathematical text", as used in mathematical practice through the ages, seems to be more appropriate. However, no commonly adopted formal notion of mathematical text has emerged so far.In this paper, we propose a formalism which aims to reflect natural (human) style and structure of mathematical argument, yet to be appropriate for automated processing: principally, verification of its correctness (we consciously use the word rather than "soundness" or "validity").We consider mathematical texts that are formalized in the ForTheL language (brief description of which is also given) and we formulate a point of view on what a correct mathematical text might be. Logical notion of correctness is formalized with the help of a calculus. Practically, these ideas, methods and algorithms are implemented in a proof assistant called SAD. We give a short description of SAD and a series of examples showing what can be done with it.