Predicate Logic

Predicate logic builds up from propositional logic by introducing quantifiers and predicate-subject statements. It allows defining a domain or set that elements belong to, and create logical statements using those elements

Predicate logic consists of:

• Predicates
• Logical Quantifiers
• Terms, which include:
  • Functions
  • Variables
  • Constants

Predicates §

See Predicate

Terms §

See Term

Logical Quantifiers §

• Universal Quantifier
• Existential Quantifier

See Logical Quantifier

Converting Natural Language to Predicate Logic §

1. Identify parts of speech (nouns, verbs, adjectives, etc. )
2. Map:
   1. Proper nouns to constants (“Rhonda”, “Paris”, etc.)
   2. Verbs (along with any adverbs or adjectives) to predicates (“Is mortal”, “runs quickly”)
   3. Relative clauses to functions (“(something) of”,“child of”)
   4. Indefinite pronouns & improper nouns to variables (“human”, “thing”)
3. Connect Quantifying words to logical quantifiers:
   1. Every/all to universal quantifier ($\forall$). Also nouns in plural ‘humans are mortal’ implies every human is mortal.
   2. ‘Some’, ‘there exists’ to existential quantifier ($\exists$)

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Some examples: