We present a DNA-based implementation of reaction system with molecules encoding elements of the propositional logic, that is, propositions and formulas. The protocol can perform inference steps using, for example, modus ponens and modus tollens rules and de Morgan's laws. The set of the implemented operations allows for inference of formulas using the laws of natural deduction. The system can also detect whether a certain proposition a can be deduced from the basic facts and given rules. The whole protocol is fully autonomous; that is, after introducing the initial set of molecules, no human assistance is needed. Only one restriction enzyme is used throughout the inference process. Unlike some other similar implementations, our improved design allows representing simultaneously a fact a and its negation ~a, including special reactions to detect the inconsistency, that is, a simultaneous occurrence of a fact and its negation. An analysis of correctness, completeness, and complexity is included.

Department of Math and Computer Science University of Lodz 90238 Łódź Poland

Research Institute of the IT4Innovations Centre of Excellence Faculty of Philosophy and Science Silesian University in Opava 74601 Opava Czech Republic