Use of abstraction and logic in mathematics

Olga Moreira

• Publisher: Arcler Press
• Year: 2023
• Topic: Mathematics
• eBook ISBN:
  9781774697009
• Subtopic: Logic in Mathematics
• Index: Mathematics

"The Use of Abstraction and Logic in Mathematics" is an edited book consisting of 16 contemporaneous open-access articles that are essentially devoted to mathematical logic research, from classical to non-classical logical systems, from algebraic logic to fuzzy logic. The book addresses the following mathematical logic topics: first-order and higher-order logic; as well as infinitary, description, modal; fixed-point, algebraic and fuzzy logic. This book also includes examples of practical applications of logical systems in link prediction and image processing tasks, as well as in the training of neural networks and artificial intelligence. The intended audience of this book is undergraduate and graduate students, as well as junior researchers. Familiarity with first-order and higher-order logics, as well as set theory, and algebra is essential to grasp the concepts and methods described in this book.

Table of contents

• Cover
• Title Page
• Copyright
• DECLARATION
• ABOUT THE EDITOR
• TABLE OF CONTENTS
• List of Contributors
• List of Abbreviations
• Preface
• Chapter 1 Classical Logic and Quantum Logic with Multiple and Common Lattice Models
• Chapter 2 A Novel Categorical Approach to Semantics of Relational First-Order Logic
• Chapter 3 Infinitary Classical Logic: Recursive Equations and Interactive Semantics
• Chapter 4 Formalization of Linear Space Theory in the Higher-Order Logic Proving System
• Chapter 5 Language and Proofs for Higher-Order SMT (Work in Progress)
• Chapter 6 Alternation Is Strict For Higher-Order Modal Fixpoint Logic
• Chapter 7 Bisimulation in Inquisitive Modal Logic
• Chapter 8 Graphical Sequent Calculi for Modal Logics
• Chapter 9 Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems
• Chapter 10 Fuzzy Logic versus Classical Logic: An Example in Multiplicative Ideal Theory
• Chapter 11 Link Prediction Using A Probabilistic Description Logic
• Chapter 12 Reasoning about Social Choice and Games in Monadic Fixed-Point Logic
• Chapter 13 Formal Analysis of 2D Image Processing Filters using Higher-order Logic Theorem Proving
• Chapter 14 GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network
• Chapter 15 Design of a Computable Approximate Reasoning Logic System for AI
• Chapter 16 On the Possibility of Correct Concept Learning in Description Logics
• Index
• Back Cover