This book is intended to introduce you to some of the most important concepts and tools of logic. Our goal is to provide detailed and systematic answers to the questions raised above. We want you to understand just how the laws of logic follow inevitably from the meanings of the expressions we use to make claims. Convention is crucial in giving meaning to a language, but once the meaning is established, the laws of logic follow inevitably.
More particularly, we have two main aims. The first is to help you learn a new language, the language of first-order logic. The second is to help you learn about the notion of logical consequence, and about how one goes about establishing whether some claim is or is not a logical consequence of other accepted claims. While there is much more to logic than we can even hint at in this book, or than any one person could learn in a lifetime, we can at least cover these most basic of issues.
Following are the few topic covered in this language, proof and logic book
- Propositional Logic
- The Logic of Atomic Sentences
- The Boolean Connectives
- Quantifiers
- Introduction to Quantification
- The Logic of Quantifiers
- Multiple Quantifiers
- Methods of Proof for Quantifiers
- Formal Proofs and Quantifiers
- Applications and Metatheory
- First-order Set Theory
- Mathematical Induction
- Advanced Topics in Propositional Logic
- Advanced Topics in FOL
- Completeness and Incompleteness
