## Tags
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## Main resources
-
- <iframe src="https://en.wikipedia.org/wiki/Logic" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe>
## Landscapes
- [[Classical logic]]
- [[Nonclassical logic]]
- [[Mathematical logic]]
- [[Formal logic]]
- - [Computability logic](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Dynamic_semantics "Dynamic semantics") interprets formulas as update functions, opening the door to a variety of nonclassical behaviours
- [Many-valued logic](https://en.wikipedia.org/wiki/Many-valued_logic "Many-valued logic") rejects bivalence, allowing for [truth values](https://en.wikipedia.org/wiki/Truth_value "Truth value") other than true and false. The most popular forms are [three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic "Three-valued logic"), as initially developed by [Jan Łukasiewicz](https://en.wikipedia.org/wiki/Jan_%C5%81ukasiewicz "Jan Łukasiewicz"), and infinitely-valued logics such as [fuzzy logic](https://en.wikipedia.org/wiki/Fuzzy_logic "Fuzzy logic"), which permit any real number between 0 and 1 as a truth value.
- [Intuitionistic logic](https://en.wikipedia.org/wiki/Intuitionistic_logic "Intuitionistic logic") rejects the [law of the excluded middle](https://en.wikipedia.org/wiki/Law_of_the_excluded_middle "Law of the excluded middle"), [double negation elimination](https://en.wikipedia.org/wiki/Double_negation_elimination "Double negation elimination"), and part of [De Morgan's laws](https://en.wikipedia.org/wiki/De_Morgan%27s_laws "De Morgan's laws");
- [Linear logic](https://en.wikipedia.org/wiki/Linear_logic "Linear logic") rejects [idempotency](https://en.wikipedia.org/wiki/Idempotency "Idempotency") of [entailment](https://en.wikipedia.org/wiki/Logical_consequence "Logical consequence") as well;
- [Paraconsistent logic](https://en.wikipedia.org/wiki/Paraconsistent_logic "Paraconsistent logic") (e.g., [relevance logic](https://en.wikipedia.org/wiki/Relevance_logic "Relevance logic")) rejects the [principle of explosion](https://en.wikipedia.org/wiki/Principle_of_explosion "Principle of explosion"), and has a close relation to [dialetheism](https://en.wikipedia.org/wiki/Dialetheism "Dialetheism");
- [Quantum logic](https://en.wikipedia.org/wiki/Quantum_logic "Quantum logic")
- [Relevance logic](https://en.wikipedia.org/wiki/Relevance_logic "Relevance logic"), [linear logic](https://en.wikipedia.org/wiki/Linear_logic "Linear logic"), and [non-monotonic logic](https://en.wikipedia.org/wiki/Non-monotonic_logic "Non-monotonic logic") reject monotonicity of entailment;
- [Non-reflexive](https://en.wikipedia.org/wiki/Reflexive_relation "Reflexive relation") logic (also known as ["Schrödinger logics"](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_logic "Schrödinger logic")) rejects or restricts the [law of identity](https://en.wikipedia.org/wiki/Law_of_identity "Law of identity");[[3]](https://en.wikipedia.org/wiki/Non-classical_logic#cite_note-3)
## Written by AI (may include factually incorrect information)
- 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.