Unconventional Algorithms: Complementarity of Axiomatics and Construction
Open Access
- 25 October 2012
- Vol. 14 (11), 2066-2080
- https://doi.org/10.3390/e14112066
Abstract
In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches.This publication has 21 references indexed in Scilit:
- AxiomatizationPublished by Wiley ,2017
- The Representation of Inconsistent Knowledge in Advanced Knowledge Based SystemsLecture Notes in Computer Science, 2011
- Computation theories: An axiomatic approach to recursion on general structuresPublished by Springer Science and Business Media LLC ,2006
- Society of mind: A response to four reviewsArtificial Intelligence, 1991
- Knowledge Representation: Features of KnowledgePublished by Springer Science and Business Media LLC ,1987
- From absolute to local mathematicsSynthese, 1986
- Abstract computability on algebraic structuresPublished by Springer Science and Business Media LLC ,1981
- Storage Modification MachinesSIAM Journal on Computing, 1980
- Axiomatic Recursive Function TheoryPublished by Elsevier BV ,1971
- Computability of Recursive FunctionsJournal of the ACM, 1963