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The Scientific World Journal
Volume 2014, Article ID 834237, 10 pages
http://dx.doi.org/10.1155/2014/834237
Research Article

The Laws of Natural Deduction in Inference by DNA Computer

1Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech Republic
2Department of Math and Computer Science, University of Lodz, 90238 Łódź, Poland

Received 10 January 2014; Accepted 26 March 2014; Published 3 July 2014

Academic Editor: Lin He

Copyright © 2014 Łukasz Rogowski and Petr Sosík. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.