Causal induction about contingency information has been the subject of debates, between the power PC theory, associative learning theory, and symmetry bias theory. Whereas most researchers in the subject area agree that cognitive bias is normative induction process overestimating particular cause-effect associations, the question remains how the cognitive bias is originated in humans' behaviors. This article offers a dynamical logic called ad-hoc logic, based on a lattice (topped intersection structure), that is continuously removing and/or adding its own elements. The ad-hoc logic implements the negotiation process between the system of representations (type) and that of objects (token). The asymmetry between types and tokens embedded in the ad-hoc logic can paradoxically lead to symmetry bias. The model is consistent with experimental results of causal judgments in literature.