⚛️ (Atomic) Formula (predicate calculus)

=== a statement about individuals of a term==

Characteristics

• Unites reference and predication:
  • reference to individuals
  • predication of properties or relations

Properties

• Completeness
  • A formula is closed (= ☑️ Sentence (Predicate Calculus), when it contains no unbound individual variables
    • e.g. incomplete: Ax ∧ Vxb
    • e.g. complete: ∃x (Ax ∧ Vxb)
    • → bind them through quantifiers
  • Otherwise, it is open
  • → Only closed formulas can make statements

Notation

• Tall letter from the beginning of the Latin alphabet
  • e.g., “A”, “B”

📖 Example:

• $P{t}_1,t_2...t_n$
  • $P$: 👉 Predicate symbol
  • $t_n$: 🔸 Term