Includes index.

Chapter 1 Classical Logic and Quantum Logic with Multiple and Common Lattice Models 1 -- Chapter 2 A Novel Categorical Approach to Semantics of Relational First-Order Logic 31 -- Chapter 3 Infinitary Classical Logic: Recursive Equations and Interactive Semantics 71 -- Chapter 4 Formalization of Linear Space Theory in the Higher-Order Logic Proving System 99 -- Chapter 5 Language and Proofs for Higher-Order SMT (Work in Progress) 111 -- Chapter 6 Alteration is Strict for Higher-Order Modal Fixpoint Logic 123 -- Chapter 7 Bisimulation in Inquisitive Modal Logic 149 -- Chapter 8 Graphical Sequent Calculi for Modal Logics 149 -- Chapter 9 Categorial Abstract Algebraic Logic: Meet-Combination of Logical Systems 191 -- Chapter 10 Fuzzy Logic versus Classical Logic: An Example in Multiplicative Ideal Theory 213 -- Chapter 11 Link Prediction Using a Probabilistic Description Logic 223 -- Chapter 12 Reasoning about Social Choice and Games in Monadic Fixed-Point Logic 247 -- Chapter 13 Formal Analysis of 2D Image Processing Filters using Higher-order Logic Theorem Proving 271 -- Chapter 14 GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network 295 -- Chapter 15 Design of a Computable Approximate Reasoning Logic System for AI 335 -- Chapter 16 On the Possibility of Correct Concept Learning in Description Logics 363 -- Index 395

"Abstraction and logic are the core foundation of mathematics. One of the most important aspects of mathematics is the formulation and proving of theorems. Logic as a foundation of mathematics provides a language for the formulation of theorems and for constructing mathematical proofs. There are many different logics, they differ in how mathematics can be expressed in them. In propositional, for instance, the fundamental logical units are declarative statements (prepositions) that can be either true or false value. This is the simplest and oldest form of mathematical logic that was developed to deal with relations between propositions, and allows the construction of compound propositions by introducing logical connectives such as conjunction ("and"), disjunction ("or"), negation ("not"), and conditions ("if", "else"). The first-order logic, in addition to those, also covers predicates and quantification. It uses variables as well as quantifies and can deal with non-logical objects. Higher-order logic extends the capabilities of first-order logic, by having stronger semantics. It features higher-order predicates, and unlike the first-order, allows the definition of predicate quantifiers and/or function quantifiers. Logic systems constitute a powerful method for representing knowledge and formalizing natural language into a computable format. They can be implemented via software and hardware. They are the basis of computer automation. We can now program computers to assists us in solving mathematical and scientific problems. The implementation and development of logical systems have allowed important breakthroughs in many scientific fields and engineering. It paved the way for the emergence of data science, machine learning, artificial intelligence, and more. Stronger logic systems have been developed, the infinitary, modal and quantum logical systems are a few examples of such. This book is focused on the description and implementation of classical and non-classical logical systems, as well as their applications." -- Provided by the publisher

English