Logic
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Logic
Foundations of logic.
Definitions
- Formal logic
- deductive reasoning
- bound by structured argumentation with defined rules (e.g syllogisms, symbolic logic)
- can be represented in mathematical form
- used in philosophy, mathematics and computer science
- Informal logic
- inductive reasoning
- prone to logical fallacies
- not bound by strict formal structure
- used in debates, legal arguments and everyday reasoning
Symbolic logic
A branch of formal logic.
-
Conjunction
- AND
- True if and only if both operands are True
- symbol:
∧
-
Disjunction
- OR
- True if at least one operand is True, including both
- symbol:
∨
-
Exclusive Disjunction
- XOR
- True if one operand is true, but not both
- symbol:
⊕
-
Negation
- NOT
- Inverts the truth value of the operand
- symbol:
¬
-
Implication
- IF ... THEN ...
- True unless a true statement implies a false one
- symbol:
→
-
Coimplication
- IF AND ONLY IF
- Biconditional, True if both operands have the same truth value
- symbol:
↔
Truth table
Proposition: A and B are truth values.
| Scenario | A | B | ¬A | A ∧ B | A ∨ B | A ⊕ B | A → B | A ↔ B |
|---|---|---|---|---|---|---|---|---|
| #1 | T | T | F | T | T | F | T | T |
| #2 | T | F | F | F | T | T | F | F |
| #3 | F | T | T | F | T | T | T | F |
| #4 | F | F | T | F | F | F | T | T |
More on
- Classical Logic by Stanford Encyclopedia of Philosophy
- Informal Logic by Stanford Encyclopedia of Philosophy
- Logic and Ontology by Stanford Encyclopedia of Philosophy
- Difference between Formal and Informal Logic? by r/philosophy
- Inductive Reasoning by ScienceDirect
- Deductive Reasoning by ScienceDirect
- Can anyone explain inductive vs deductive reasoning to me. by r/explainlikeimfive
- What's the difference between deductive reasoning and inductive reasoning? by LIVESCIENCE
- 2.1: Introduction to Formal Logic by LibreTexts Mathematics
- Logical Fallacies by Purdue University
- thou shalt not commit logical fallacies by yourlogicalfallacyis.com
- Philosophy 103: Introduction to Logic, The Language of Symbolic Logic by philosophy.lander.edu
- Symbolic Logic Overview, List & Examples by Study.com
- Symbolic Logic (or Algebra meets Logic) by Kyle Shevlin
- Chapter 3: Symbolic Logic and Proofs by Oscar Levin
- ATS2866 - Symbolic logic by Monash University Handbook
- Truth Tables, Tautologies, and Logical Equivalences by Bruce Ikenaga
- 2.2: Introduction to Truth Tables by LibreTexts Mathematics
- Truth Table Generator by Stanford University