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.
Logic of graphs Logic of graphs In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using logical formulas. There are several variations in the types of logical operation that can be used in these formulas. The first order logic of graphs concerns formulas in which the variables and predicates concern individual vertices and edges of a graph, while monadic second order graph logic allows quantification over sets of vertices or edges. A sentence formula_1 may be true for some graphs, and false for others; a graph formula_2 is said to