Reactions catalyzed by artificial allosteric enzymes, chimeric proteins with fused biorecognition and catalytic units, were used to mimic multi‐input Boolean logic systems. The catalytic parts of the systems were represented by pyrroloquinoline quinone‐dependent glucose dehydrogenase (PQQ‐GDH). Two biorecognition units, calmodulin or artificial peptide‐clamp, were integrated into PQQ‐GDH and locked it in the OFF or ON state respectively. The ligand‐peptide binding cooperatively with Ca2+ cations to a calmodulin bioreceptor resulted in the enzyme activation, while another ligand‐peptide bound to a clamp‐receptor inhibited the enzyme. The enzyme activation and inhibition originated from peptide‐induced allosteric transitions in the receptor units that propagated to the catalytic domain. While most of enzymes used to mimic Boolean logic gates operate with two inputs (substrate and co‐substrate), the used chimeric enzymes were controlled by four inputs (glucose – substrate, dichlorophenolindophenol – electron acceptor/co‐substrate, Ca2+ cations and a peptide – activating/inhibiting signals). The biocatalytic reactions controlled by four input signals were considered as logic networks composed of several concatenated logic gates. The developed approach allows potentially programming complex logic networks operating with various biomolecular inputs representing potential utility for different biomedical applications.