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[[Classical logic]]
[[Nonclassical logic]]
Mathematical logic
Formal logic
- Computability logic is a semantically constructed formal theory of computability—as opposed to classical logic, which is a formal theory of truth—that integrates and extends classical, linear and intuitionistic logics.
Dynamic semantics interprets formulas as update functions, opening the door to a variety of nonclassical behaviours
Many-valued logic rejects bivalence, allowing for truth values other than true and false. The most popular forms are three-valued logic, as initially developed by Jan Łukasiewicz, and infinitely-valued logics such as fuzzy logic, which permit any real number between 0 and 1 as a truth value.
Intuitionistic logic rejects the law of the excluded middle, double negation elimination, and part of De Morgan's laws;
Linear logic rejects idempotency of entailment as well;
Paraconsistent logic (e.g., relevance logic) rejects the principle of explosion, and has a close relation to dialetheism;
Quantum logic
Relevance logic, linear logic, and non-monotonic logic reject monotonicity of entailment;
Non-reflexive logic (also known as "Schrödinger logics") rejects or restricts the law of identity;[3]

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Logic is a branch of philosophy that studies the principles of correct reasoning. It's a foundational discipline for many fields, including mathematics, computer science, and linguistics. Here's a comprehensive list of various branches and sub-disciplines within logic:

1. Classical Logic¶

Propositional Logic (or Sentential Logic)
First-Order Logic (or Predicate Logic)
Second-Order and Higher-Order Logic
Syllogistic Logic (Aristotelian Logic)

2. Non-Classical Logics¶

Modal Logic (Necessity and Possibility)
Temporal Logic (Time)
Deontic Logic (Duty and Obligation)
Epistemic Logic (Knowledge and Belief)
Doxastic Logic (Belief)
Conditional Logic (If-Then Statements)

3. Mathematical Logic ¶

Set Theory
Proof Theory
Model Theory
Recursion Theory (or Computability Theory)
Constructive Logic (or Intuitionistic Logic)
Category Theory in Logic

4. Philosophical Logic¶

Philosophical Analysis of Logical Concepts
Logic and Language
Logic and Metaphysics
Logic and Epistemology

5. Symbolic Logic¶

Formal Syntax and Semantics
Symbolic Representation of Logical Formulas
Boolean Logic

6. Formal Systems¶

Axiomatic Systems
Formal Languages
Formal Proof Systems
Theorem Proving

7. Applied Logic¶

Informal Logic (Argumentation Theory)
Logic of Natural Language
Critical Thinking
Fallacies and Logical Errors
Rhetoric and Persuasion

8. Computational Logic¶

Logic Programming
Automated Reasoning
Computational Complexity of Logical Theories
Decision Procedures

9. Quantificational Logic¶

Existential and Universal Quantification
Quantifier Scope and Interpretation

10. Fuzzy Logic¶

Multi-valued Logic
Degrees of Truth
Applications in Control Systems and Artificial Intelligence

11. Paraconsistent Logic¶

Handling Contradictory Information
Dialetheism (True Contradictions)

12. Relevance Logic¶

Logical Relevance in Implication
Avoiding Paradoxes of Material Implication

13. Quantum Logic¶

Logic for Quantum Mechanics
Non-classical Probability Theory

14. Dialogic Logic¶

Logic of Dialogue and Argumentation
Interactive Proof Systems

15. History of Logic¶

Study of Historical Development and Figures in Logic

16. Bivalent and Multivalent Logics¶

Logics with More than Two Truth Values
Intermediate Truth Values

17. Bayesian Logic¶

Logic Based on Bayesian Probability

18. Inductive Logic¶

Reasoning from Specific to General
Probabilistic Reasoning

19. Counterfactual Reasoning¶

Logic of Hypotheticals and "What If" Scenarios

20. Formal Ethics¶

Deontic Logic Applied to Ethical and Moral Reasoning

Logic is a broad and diverse field that continues to evolve, adapting to new philosophical questions, mathematical developments, and computational challenges. It serves as a fundamental framework for clear thinking, problem-solving, and the pursuit of knowledge across disciplines.

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