0x00 Foundations

Logic

Propositional Logic

Predicate Logic

Modal Logic

Relation

Equality

axiom of equality

  • reflexive: for any object x, x=x
  • symmetry: for any object of the same type, if x=y, then y=x
  • transitive: for any object of the same type, if x=y,y=z, then x=z
  • substitution: for any object x,y of the same type and function f, if x=y, then f(x)=f(y), or for any property P, P(x)=P(y)