Math 2.0

Mathematical logic and foundations First-order logic Concept

Predicate logic

Builds on Propositional logicPredicate

Summary

Predicate logic extends propositional logic with variables for objects, predicates and quantifiers. Its formulas can say "for all xx" with the universal quantifier and "there exists xx" with the existential quantifier. In first-order logic, the quantifiers range over objects, not over sets of objects or predicates.

Remarks

Other names are first-order logic and predicate calculus. An example of a formula is ∀x ∃y (y>x)\forall x \, \exists y \, (y > x). Most of mathematics can be written in first-order logic with the axioms of Zermelo–Fraenkel set theory.

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To understand this page from the ground up, read these 9 pages in order. The foundations come first.

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Proposition, concept, no evidence levelPropositionconceptConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionPropositional logic, concept, no evidence levelPropositional logicconceptPredicate logic, concept, no evidence levelPredicate logicconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proposition concept
  2. Conjunction definition
  3. Disjunction definition
  4. Implication definition
  5. Negation definition
  6. Predicate definition
  7. Biconditional definition
  8. Propositional logic concept
  9. Predicate logic concept

Where this leads

52 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/First-order_logic, lead section
About this page
Tag086QKPF0A6
URIm2://086QKPF0A6
Aliasesfirst-order-logic, predicate-calculus
Kindconcept
WritingW1 stated
MSC03B10
UsesPropositional logic, Predicate
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