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.
Fragment (logic) is a reduction from the first problem to the other. An important problem in computational logic is to determine fragments of well-known logics such as first-order logic that are as expressive as possible yet are decidable or more strongly have low computational complexity. The field of descriptive complexity theory aims at establishing a link between logics and computational complexity theory, by identifying logical fragments that exactly capture certain complexity classes. Fragment (logic) In mathematical logic, a fragment of a logical language or theory is a subset of this logical language obtained by imposing syntactical restrictions on the language. Hence, the