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Branch: Logic

Logic is a discipline of mathematics which formalizes the language and methods of mathematical reasoning and examining the correctness of arguments. In this sense, logic is the metalanguage of mathematics and we start BookofProofs with this branch. Usually, in logic arguments can be either true or false. But there are also other types of logic, in which more than these two values are allowed.

Theoretical minimum (in a nutshell)

In order to start the mathematical foundations of logic, the following prerequisites are required:

• You should be acquainted with set theory, especially with their basic properties.

Concepts you will learn in this part of BookofProofs

• Basic notions to build formal systems, including alphabet, propositions, syntax and semantics.
• Different types of formal systems,
  • starting with some propositional logic, which follows the rules of Boolean algebra,
  • continuing with first order predicate logic, involving free and bound variables, functions and quantifiers
  • and giving an outlook to higher order predicate logics.
• Methods and strategies of mathematical proving.

Table of Contents

1. Part: Historical Development of Logic
2. Part: Basic Concepts of Logic
3. Part: Proof Theory
4. Part: Propositional Logic
5. Part: PL1 - First Order Predicate Logic
6. Part: Higher-Order Logics
7. Part: Gödel's Incompleteness Theorems
8. Part: Methods of Mathematical Proving
9. Part: Solving Strategies and Sample Solutions to Problems in Logic

Mentioned in:

Branches: 1 2
Motivations: 3
Parts: 4

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