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- Formal logic is a system for drawing conclusions from premises, often unfamiliar outside of mathematics and certain computer science fields.
- Mathematicians use formal logic to remove ambiguities in proofs, particularly with conditional statements like 'if A then B'.
- In formal logic, 'if A then B' implies its contrapositive 'if not B then not A', but not its inverse or converse.
- Logic can be used to construct mathematical systems, such as real numbers, from axioms without relying on physical intuition.
- Boolean algebra in computing operates on binary values with operators like NOT, AND, and OR, and can be related to set theory.
- Propositional logic deals with statements that have binary truth values and uses connectives like implication and equivalence.
- First-order logic extends propositional logic with predicates, quantifiers, and functions to generalize over objects.
- Non-standard logic systems exist, such as those rejecting the law of excluded middle, but are less commonly used.