A New Way of Defining Deductive Consequence for Modal and Predicate Logic

Studies in Logic, Vol. 13, No. 6 (2020): 1–24      PII: 1674-3202(2020)-06-0001-24

Xuefeng Wen

Abstract. Deductive consequence has been defined in various ways in modal logic and predicate logic. Though most of them can be proved to be equivalent, they have different advantages and disadvantages. We propose a new way of defining deductive consequence of axiomatic systems for modal and predicate logic, by distinguishing two kinds of rules in an axiomatic system. We argue that the new definition not only inherits all advantages of existing definitions but also unifies all six consequences in modal and predicate logic. We show some pedagogical merits of the new definition as well.