Decomposition (Mathematics), Many-valued logic, Symbolic and mathematical logic
A novel many-valued decomposition within the framework of lossless Reconstructability Analysis is presented. In previous work, Modified Recontructability Analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional Reconstructability Analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decomposition exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. In this paper, MRA is extended to many-valued logic functions, and logic structures that correspond to such decomposition are developed. It is shown that many-valued MRA can decompose many-valued functions when CRA fails to do so. Since real-life data are often manyvalued, this new decomposition can be useful for machine learning and data mining. Many-valued MRA can also be applied for the decomposition of relations.
Al-Rabadi, A., and Zwick, M. (2004). "Modified Reconstructability Analysis for Many-Valued Functions and Relations." Kybernetes, vol. 33, No. 5/6, pp. 906-920