The field of DNA computing is devoted to the creation of devices capable of processing information signals encoded on biological substrates. These signals are intended to propagate in cascades of biochemical reactions in which they naturally undergo a progressive reduction. Preventing signal reduction becomes crucial considering applications in biological environments where molecular cues are scarce. Although catalytic gates have been developed using the toehold-exchange mechanism for logic gate circuits, the matter remains unaddressed for logic reasoning devices. Inspired by the main work in biomolecular logic programming, we present a new encoding scheme for facts, rules, and queries to implement backward/forward chaining inference paths via catalytic DNA strand displacement cascades. In this context, we take advantage of fueling reactions to recover inputs, which preserve their availability to react with different implication gates. Our molecular design is thermodynamically analyzed by providing suitable sequences for the correct formation of structures. With regard to the kinetic performance, data from simulations suggest that the model operates efficiently even with identified crosstalk reactions.INDEX TERMS Catalytic reactions, DNA strand displacement, logic programming, molecular computing.