Narrow Results

In this paper we present a many-valued memory circuit based on a generalization of the R-S memory circuit known from the two-valued logical circuits.

Based on this many-valued R-S memory circuit we introduce a many-valued level-controlled memory circuit and a many-valued edge-controlled memory circuit of type “master-slave”.

We discuss problems of the stability of the circuit with respect to small errors of input and output signals as well as to small errors of the gates. We show that the stability can be preserved by restricting the set of logical values, i.e. the interval [0, 1], to a finite discrete subset of this interval.

We find the set of many-valued operations which are suitable for the implementation of the many-valued R-S memory circuit.

Let k ≥ 2, E_k := {0, 1,…, k – 1}, and let P_k denote the set of all k-valued logical functions, i.e., of maps for n = 1, 2, … We denote by P_k(2) the set of all functions of P_k whose range contains no more than two elements. The set P_k(2) is a closed set (or class) with respect to the usual superposition operations and all maximal closed subsets of P_k(2) are known. For each f ∈ P_k(2) we determine its characteristic vectors with respect to the maximal classes and give an explicit formula for the total number of the characteristic vectors in terms of the numbers of the equivalence relations on E_k. Then we show that P₃(2) has exactly 75 characteristic vectors and 33,678 classes of bases, and show that the cardinality of an arbitrary basis for P₃(2) is 3, 4 or 5.

I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.