Intelligent Computer Mathematics 11th International Conference, CICM 2018, Hagenberg, Austria, August 13-17, 2018, Proceedings

?This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Computer Mathematics, CICM 2018, held in Hagenberg, Austria, in August 2018. The 23 full papers   presented were carefully reviewed and selected from a total of 36 submissions. The papers focos on the...

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Bibliographic Details
Main Authors Rabe, Florian, Farmer, William M, Passmore, Grant O, Youssef, Abdou
Format eBook Conference Proceeding
LanguageEnglish
Published Cham Springer Nature 2018
Springer International Publishing AG
Springer International Publishing
Edition1
SeriesLecture Notes in Computer Science
Subjects
Artificial Intelligence
Artificial intelligence-Mathematics-Congresses
Computer Appl. in Social and Behavioral Sciences
Computer Science
Computers and Education
Mathematical Logic and Formal Languages
Programming Languages, Compilers, Interpreters
Programming Techniques
Special computer methods
Online AccessGet full text
ISBN3319968122
9783319968124
3319968114
9783319968117
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-96812-4

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Table of Contents:
  • Automated Determination of Isoptics with Dynamic Geometry -- 1 Introduction -- 2 Isoptic Curves -- 2.1 Orthoptics of Conics -- 2.2 Generalization to Other Curves -- 3 The First Approach -- 4 The Second Approach -- 4.1 Implementation Issues -- 4.2 Isoptics -- 5 Conclusion -- References -- Biform Theories: Project Description -- 1 Motivation -- 2 Background Ideas -- 3 Project Objectives -- 4 Work Plan Status -- 5 Related Work -- 6 Conclusion -- References -- A Coq Formalization of Digital Filters -- 1 Introduction -- 2 Digital Filters -- 2.1 Signals and Operations -- 2.2 Linear Time Invariant Filters -- 2.3 Impulse Response -- 2.4 Constant-Coefficient Difference Equation -- 3 Formalization -- 3.1 Signals and Filters -- 3.2 Recursion over Z -- 3.3 Adapting Existing Libraries to Relative Indexes -- 4 Filter Realizations -- 4.1 Direct Form I -- 4.2 Direct Form II -- 4.3 State-Space -- 5 Error Analysis Tools -- 5.1 Error Filter -- 5.2 Worst-Case Peak Gain Theorem -- 6 Conclusions and Perspectives -- References -- MathTools: An Open API for Convenient MATHML Handling -- 1 Introduction -- 2 Related Work -- 3 MathTools -- 4 Conclusion and Future Work -- References -- Aligator.jl - A Julia Package for Loop Invariant Generation -- 1 Introduction -- 2 Background and Notation -- 3 System Description of Aligator.jl -- 4 Experimental Evaluation -- 5 Conclusion -- References -- Enhancing ENIGMA Given Clause Guidance -- 1 ENIGMA: Efficient Learning of Given Clause Guidance -- 2 Enhanced ENIGMA Features and Classifiers -- 3 Experimental Evaluation -- 4 Software Distribution -- References -- Formalized Mathematical Content in Lecture Notes on Modelling and Analysis -- 1 Introduction -- 2 Examples of Formalizations -- 2.1 Conditions -- 2.2 Mappings -- 2.3 Parametric Conditions -- 2.4 Theorems -- 2.5 Proofs -- 2.6 Spaces, Structures and Models -- 3 Conclusions
  • 2 Technical Background Information -- 3 Collaboratively Discovering a Mathematical Algorithm -- 3.1 Example of Collaborative Algorithm Discovery -- 3.2 Distributed Cognition Foundation -- 3.3 Collaborative Computation Model (CCM) -- 3.4 Formalized Hypothesis on Algorithm Discovery -- 4 Formally Describing Learned Algorithmic Knowledge -- 5 Implementing Mathematical Social Machines -- 5.1 MathChat Features for Realizing the Social Machines -- 5.2 Application in Online Education and Pilot Investigation -- 6 Discussion, Limitations and Future Directions -- References -- Automatically Finding Theory Morphisms for Knowledge Management -- 1 Introduction -- 2 Preliminaries: MMT and Views -- 3 Intra-Library View Finding -- 3.1 Preprocessing -- 3.2 Search -- 3.3 Optimizations -- 3.4 Implementation -- 4 Inter-Library View Finding -- 4.1 The PVS/NASA Library -- 4.2 Implementation -- 5 Conclusion -- References -- Goal-Oriented Conjecturing for Isabelle/HOL -- 1 Introduction -- 2 System Description -- 2.1 Identifying Valuable Conjectures via Proof Search -- 2.2 Conjecturing -- 3 Conclusion -- References -- Knowledge Amalgamation for Computational Science and Engineering -- 1 Introduction and Motivation -- 2 Meta-Modeling and Simulation -- 2.1 The MaMoReD Approach -- 2.2 Poisson's Equation -- 2.3 Theory Graphs -- 2.4 MoSIS: Creating ExaSlang Layer 0 -- 3 MoSIS: Combining MaMoReD and ExaStencils -- 3.1 A Theory Graph for PDE Knowledge -- 3.2 Automating Model Knowledge Amalgamation -- 3.3 Implementation: Realizing MoSIS via Jupyter and Mmt -- 4 Conclusion and Future Work -- References -- Validating Mathematical Theorems and Algorithms with RISCAL -- 1 Introduction -- 2 Checking Theorems and Algorithms -- 3 Current and Further Work -- References -- First Experiments with Neural Translation of Informal to Formal Mathematics -- 1 Introduction: Autoformalization
  • References -- Isabelle Import Infrastructure for the Mizar Mathematical Library -- 1 Introduction -- 2 Existing Mizar Exports -- 3 Isabelle and the Mizar Object Logic -- 4 Isabelle Import Infrastructure -- 5 Mizar-Style Proof Development in Isabelle -- 6 Combining the Syntactic and Semantic Representations of Mizar -- 6.1 Procedure Overview -- 6.2 Background Information -- 6.3 Definitions -- 6.4 Redefinitions -- 7 Conclusion -- References -- Discourse Phenomena in Mathematical Documents -- 1 Introduction -- 2 The Eye-Tracking Study -- 3 Patterns in the Gaze Plots -- 4 Patterns in the Elicited Data -- 4.1 Structure-Driven Areas of Interest -- 4.2 Math-Driven Areas of Interest -- 4.3 What are Cognitive Units (Words) in Math? -- 5 A Nascent Theory for Mathematical Documents -- 5.1 Design Application: Interactive Documents -- 6 Conclusion -- References -- Finding and Proving New Geometry Theorems in Regular Polygons with Dynamic Geometry and Automated Reasoning Tools -- 1 Introduction -- 2 Mathematical Background -- 2.1 Constructibility -- 2.2 An Algebraic Formula for the Vertices -- 3 Example Statements -- 3.1 Lengths in a Regular Pentagon -- 3.2 Lengths in a Regular 11-gon -- 3.3 Implementation in GeoGebra -- 4 Conclusion and Future Work -- References -- Gröbner Bases of Modules and Faugère's F4 Algorithm in Isabelle/HOL -- 1 Introduction -- 1.1 Related Work -- 2 Multivariate Polynomials -- 2.1 Power-Products -- 2.2 Polynomials -- 3 Gröbner Bases and Buchberger's Algorithm -- 3.1 Polynomial Reduction -- 3.2 Gröbner Bases -- 3.3 An Algorithm Schema for Computing Gröbner Bases -- 3.4 Buchberger's Algorithm -- 4 Faugère's F4 Algorithm -- 5 Further Features -- 5.1 Reduced Gröbner Bases -- 5.2 Gröbner Bases of Syzygy Modules -- 6 Conclusion -- References -- MathChat: Computational Mathematics via a Social Machine -- 1 Introduction
  • Intro -- Preface -- Organization -- Contents -- System Description: XSL-Based Translator of Mizar to LaTeX -- 1 Introduction -- 2 Summary of the Old Mizar-to-LaTeX Translation -- 3 Description of the New Technology -- 3.1 addformat.xsl -- 3.2 addtranslation.xsl -- 3.3 varrepr.xsl -- 3.4 multipred.xsl -- 3.5 transitive.xsl -- 3.6 compress.xsl -- 3.7 recognize-programs.xsl -- 3.8 article2latex.xsl and article2html.xsl -- 3.9 Remote Service and Processing Times -- 4 Conclusion and Future Work -- References -- Translating the IMPS Theory Library to MMT/OMDoc -- 1 Introduction -- 2 Preliminaries -- 2.1 Preliminaries: LUTINS -- 2.2 Preliminaries: IMPS -- 2.3 Preliminaries: OMDoc/MMT -- 3 Implementation -- 3.1 The LUTINS Theory in LF -- 3.2 Translation -- 4 Applications -- 5 Conclusion -- References -- Using the Isabelle Ontology Framework -- 1 Introduction -- 2 Background: The Isabelle System -- 3 Isabelle/DOF -- 4 Modeling Ontologies in Isabelle/DOF -- 4.1 The Scholar Paper Scenario: Eating One's Own Dog Food -- 4.2 The Math-Exam Scenario -- 4.3 The Certification Scenario Following CENELEC -- 5 Ontology-Based IDE Support -- 5.1 A Scholarly Paper -- 5.2 CENELEC -- 6 Conclusion and Related Work -- References -- Automated Symbolic and Numerical Testing of DLMF Formulae Using Computer Algebra Systems -- 1 Problem and Current State -- 2 Extraction of DLMF Formulae -- 2.1 First Extraction Scan -- 2.2 Second Extraction Scan -- 2.3 Ongoing Semantic Enhancement for Second Extraction Scan -- 3 CAS Verification Procedure for DLMF Formulae -- 3.1 Symbolic Verification of DLMF Formulae -- 3.2 Constraint Handling -- 3.3 Numerical Verification of DLMF Formulae -- 4 Summary -- References -- Concrete Semantics with Coq and CoqHammer -- 1 Introduction -- 2 Concrete Semantics with Isabelle/HOL -- 3 Coq and Coq Automation -- 4 Case Studies -- 5 Conclusion -- References
  • 2 Neural Translation -- 2.1 The Seq2seq Model -- 2.2 RNN and the RNN Memory Cell -- 2.3 Attention Mechanism -- 3 The Informalized Dataset -- 4 Applying Neural Translation to Mizar -- 4.1 Data Preprocessing -- 4.2 Division of Data -- 4.3 Choosing Hyperparameters -- 5 Evaluation -- 5.1 Choosing the Best Memory Cell and Attention Mechanism -- 5.2 The Effect of Optimizers, Residuals and Encodings with Respect to Layers -- 5.3 The Effect of the Number of Units and the Final Result -- 5.4 Greedy Covers and Edit Distances -- 5.5 Translating from Mizar to LaTeX -- 6 A Translation Example -- 7 Conclusion and Future Work -- References -- Deep Learning for Math Knowledge Processing -- 1 Introduction -- 2 Objectives of the Project -- 3 Significance and Applications of the Project -- 4 Foundations and Related Work -- 4.1 The Parts-of-Math Tagger -- 4.2 Lcolor push gray 0color popTto10AT.4exExml -- 5 The Datasets to Be Collected, Created and Used -- 6 Samples of Tagging and Disambiguation Algorithms -- 6.1 Tagging and Semantic Extraction -- 6.2 Disambiguation -- 6.3 Classification-Based Disambiguation of Math-Tagging -- 7 DNN's for Math Sequence-to-Sequence Translation -- 8 Testing and Performance Evaluation -- 9 Stages of the Project -- 10 Current State of the Project -- References -- Author Index