Infinitary logic logical axiom, an element of T, or is deduced from previous statements using a rule of inference. As before, all rules of inference in finitary logic can be used, together with an additional one: The logical axiom schemata specific to infinitary logic are presented below. Global schemata variables: formula_3 and formula_18 such that formula_23. The last two axiom schemata require the axiom of choice because certain sets must be well orderable. The last axiom schema is strictly speaking unnecessary as Chang's distributivity laws imply it, however it is included as a natural way to allow natural weakenings to the logic.
Logical hexagon "One of two things, either whatever x may be, if x is a man, then x is white or whatever x may be, if x is a man, then x is non-white." The logical hexagon may be interpreted in various ways, including as a model of traditional logic, quantifications, modal logic, order theory, or paraconsistent logic. The logical hexagon may be interpreted as a model of modal logic such that It has been proven that both the square and the hexagon, followed by a “logical cube”, belong to a regular series of n-dimensional objects called “logical bi-simplexes of dimension n.”