first order logic (original) (raw)

• •
  ¬⁢ϕ is true iff ϕ is not true
• •
  ϕ∨ψ is true if either ϕ is true or ψ is true
• •
  ∀x⁢ϕ⁢(x) is true iff ϕxt is true for every object t (where ϕxt is the result of replacing every unbound occurrence of x in ϕ with t)
• •
  ϕ∧ψ is the same as ¬⁡(¬⁢ϕ∨¬⁢ψ)
• •
  ϕ→ψ is the same as (¬⁢ϕ)∨ψ
• •
  ϕ↔ψ is the same as (ϕ→ψ)∧(ψ→ϕ)
• •
  ∃x⁢ϕ⁢(x) is the same as ¬⁢∀x⁢¬⁢ϕ⁢(x)

However languages with slightly different quantifiers and connectives are sometimes still called first order as long as there is only one type.