Stepping Theories of Active Logic with Two Kinds of Negation

This paper formulates a stepping theory formalism with two kinds of negation dealing with one of the areas of Active Logic, a new kind of logic aimed at performing practical tasks in real time knowledge-based AI systems. In addition to the standard logical negation, the proposed formalism uses the so-called subjective negation interpreted as inability to arrive at some conclusion through reasoning by a current time. The semantics of the proposed formalism is defined as an~argumentation structure.