Study Notes for Logic
2024-07-06 21:10:51 0 Report
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Outline/Content
Introduction to Logic
Definition of Logic
Importance and Applications of Logic
Basic Terminology: Propositions, Arguments, Validity, Soundness
Propositional Logic
Propositions: Simple and Compound
Logical Connectives: AND, OR, NOT, IMPLIES
Truth Tables
Logical Equivalences
Predicate Logic
Quantifiers: Universal (∀) and Existential (∃)
Predicates and Variables
Logical Inference: Modus Ponens, Modus Tollens, Universal Instantiation, Existential Generalization
Boolean Algebra
Boolean Functions
Basic Laws of Boolean Algebra: Commutative, Associative, Distributive, Identity, Complement
Boolean Expressions and Simplification Techniques
Logical Reasoning
Deductive Reasoning vs. Inductive Reasoning
Formal Proofs: Direct Proof, Proof by Contradiction, Proof by Contrapositive
Logical Fallacies
Sets and Relations
Set Theory: Sets, Subsets, Union, Intersection, Complement
Relations: Types of Relations, Reflexivity, Symmetry, Transitivity
Functions: Definition, Domain, Codomain, Range
Modal Logic
Modal Operators: Necessity (☐) and Possibility (◇)
Possible Worlds Semantics
Modal Axioms and Rules of Inference
Logical Systems
Classical Logic vs. Non-Classical Logic
Modal Logic, Temporal Logic, Fuzzy Logic
Paraconsistent Logic and Relevance Logic
Philosophical Foundations
Logic and Ontology
Logic and Epistemology
Logic and Ethics
Applications of Logic
Computer Science: Boolean Logic, Programming, Artificial Intelligence
Mathematics: Set Theory, Proof Theory
Philosophy: Philosophical Logic, Argumentation
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