## Tags - Part of: - Related: - Includes: - Additional: ## 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.