Vector logics: the matrix-vector representation of logical calculus

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually produces a CA rule table without providing a clear understanding of the structure of the neighborhood or the CA rule. In this paper, a new identification method based on using a modified orthogonal least squares or CA-OLS algorithm to detect the neighborhood structure and the underlying polynomial form of the CA rules is proposed. The Quine-McCluskey method is then applied to extract minimum Boolean expressions from the polynomials. Spatio-temporal patterns produced by the evolution of 1D, 2D, and higher dimensional binary CAs are used to illustrate the new algorithm, and simulation results show that the CA-OLS algorithm can quickly select both the correct neighborhood structure and the corresponding rule.

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Identification of the neighborhood and CA rules from spatio-temporal CA patterns

A formal analysis is made of how to project an attribute criterion into the hierarchical classes model for object by attribute data proposed by De Boeck and Rosenberg The projection is conceptualized as the prediction of the attribute criterion by means of a logical rule defined on the basis of attribute combinations from the model Eliminative and constructive strategies are proposed to find logical rules with maximal predictive power and minimal formula complexity Logical analyses of a real data set are reported and compared with a logistic regression to demonstrate the usefulness of the logical strategies, and to show the complementarity of logical and probabilistic approaches

Projection of a binary criterion into a model of hierarchical classes

Algorithm concept for information processing and pattern recognition involving incomplete or uncertain data

Communication Fuzzy Algorithms

In this paper, binary-vector Boolean algebra, a generalization of ordinary Boolean algebra [6], is introduced. In this algebra, every element is represented by a binary vector and in addition to ordinary AND, OR, and NOT operations, a new operation called the rotation operation which rotates (rightward or leftward) the components of a binary vector is introduced. Moreover, the NOT or COMPLEMENTATION operation is extended to a more general operation called the generalized complement which includes the total complement (ordinary complement), the null complement (no complement), and newly introduced partial complements. Because of this generalization, all axioms and theorems of ordinary Boolean algebra are generalized. In particular, it is shown that DeMorgan's theorem, Shannon's theorem, and the expansion theorem are generalized into more general forms which include their corresponding ordinary version as a special case. It is also shown that any multivalued logic truth table can be represented by a vector Boolean function. Three compact canonical (sum-of-products and product-of-sums) forms of this function are presented.

Vector Boolean Algebra and Calculus

Logic and Algorithms: With Applications to the Computer and Information Sciences (Robert R. Korfhage)

Advances in Programming & Non-Numerical Computation (L. Fox)

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Logic and Algorithms: With Applications to the Computer and Information Sciences (Robert R. Korfhage)

Advances in Programming & Non-Numerical Computation (L. Fox)