The Laws of Natural Deduction in Inference by DNA Computer
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 implemente...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/834237 |
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| _version_ | 1832567824899375104 |
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| author | Łukasz Rogowski Petr Sosík |
| author_facet | Łukasz Rogowski Petr Sosík |
| author_sort | Łukasz Rogowski |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ba5aee4ba146412199310bb396ba3228 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-ba5aee4ba146412199310bb396ba32282025-02-03T01:00:26ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/834237834237The Laws of Natural Deduction in Inference by DNA ComputerŁukasz Rogowski0Petr Sosík1Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech RepublicResearch Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech RepublicWe 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.http://dx.doi.org/10.1155/2014/834237 |
| spellingShingle | Łukasz Rogowski Petr Sosík The Laws of Natural Deduction in Inference by DNA Computer The Scientific World Journal |
| title | The Laws of Natural Deduction in Inference by DNA Computer |
| title_full | The Laws of Natural Deduction in Inference by DNA Computer |
| title_fullStr | The Laws of Natural Deduction in Inference by DNA Computer |
| title_full_unstemmed | The Laws of Natural Deduction in Inference by DNA Computer |
| title_short | The Laws of Natural Deduction in Inference by DNA Computer |
| title_sort | laws of natural deduction in inference by dna computer |
| url | http://dx.doi.org/10.1155/2014/834237 |
| work_keys_str_mv | AT łukaszrogowski thelawsofnaturaldeductionininferencebydnacomputer AT petrsosik thelawsofnaturaldeductionininferencebydnacomputer AT łukaszrogowski lawsofnaturaldeductionininferencebydnacomputer AT petrsosik lawsofnaturaldeductionininferencebydnacomputer |