What are the basic knowledge of mathematical logic?
1. Propositional logic: This is the basis of mathematical logic, which mainly studies the relationship between propositions, such as implication, equivalence, negation, etc. A proposition usually consists of a subject and a predicate, such as "All cats are mammals".
2. Predicate logic: This is an extension of propositional logic, which can handle more complex propositions, such as those with multiple variables. For example, "For all x and y, if x is greater than y, then x+ 1 is also greater than y+ 1".
3. Inference rules: This is the basic method of logical reasoning, including hypothetical reasoning, rejection reasoning, double negative rules and so on.
4. Formal system: This is a set of axioms and reasoning rules, which are used to describe and deal with specific logical structures. Common formal systems include propositional calculus and first-order predicate calculus.
5. Model theory: This is an important branch of mathematical logic, which studies how to express logical structure with specific mathematical objects (such as sets and relationships).
6. Proof theory: This is another important branch of mathematical logic, which studies how to prove the consistency of a proposition or system.
7. Computational theory: This is the cross field of mathematical logic and computer science, which studies how to design and analyze the computational process with logic.
8. Non-classical logic: This is an extension of classical logic, including modal logic, sequential logic and fuzzy logic. Used to deal with more complex reasoning problems.
The above is some introductory knowledge of mathematical logic, I hope it will help you.