We consider the use of feedback loops in the realization of multiple-valued combinational circuits. We show that the number of purely combinational configurations in an r-valued system is llr of the total number. Thus, as the radix increases, the fraction of combinational configurations decreases. We also show that, for every radix value r , there is a circuit with feedback realizing a combinat...

This paper surveys some polarity-based knowledge representational and automated reasoning techniques in the domain of many-valued logics.

This paper describes a probabilistic method for verifying the equivalence of two multiple-valued functions. Each function is hashed to an integer code by transforming it to a integer-valued polynomial and the equivalence of two polynomials is checked probabilistically. The hash codes for two equivalent functions are always the same. Thus, the equivalence of two functions can be verified with a ...

The multiple-instance learning model has received much attention recently with a primary application area being that of drug activity prediction. Most prior work on multiple-instance learning has been for concept learning, yet for drug activity prediction, the label is a real-valued affinity measurement giving the binding strength. We present extensions of k-nearest neighbors (k-NN), Citation-k...

While there has been a significant amount of theoretical and empirical research on the multiple-instance learning model, most of this research is for concept learning. However, for the important application area of drug discovery, a real-valued classification is preferable. In this paper we initiate a theoretical study of real-valued multiple-instance learning. We prove that the problem of find...

A multiple-valued transformation T from a space X to a space Y is a function assigning to each point x o f X a nonempty closed subset T(x) of F. The graph of T comprises those points (x, y) in the topological product X Y for which y belongs to T(x). All spaces to be considered shall be compact metric and all transformations T shall be upper semi-continuous, meaning that their graphs are closed,...

We propose the use of universal literals as a means of reducing the cost of multiple-valued circuits. A universal literal is any function on one variable. The target architecture is a sum-of-products structure, where sum is the truncated sum and product terms consist of the minimum of universal literals. A significant cost reduction is demonstrated over the conventional window literal. The prop...

The composition tree of a given function, when it exists, provides a representation of the function revealing all possible disjunctive decompositions, thereby suggesting a realization of the function at a minimal cost. Previously and independently, the authors had studied the class of multiplevalued functions that are fully sensitive to their variables. These functions are useful for test gener...

We contribute to the theory of implications and conjunctions related by adjointness, in multiple-valued logics. We suggest their use in Zadeh s compositional rule of inference, to interpret generalized modus ponens inference schemata. We provide new complete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunction...

Abs t rac t . The coincidence of the declarative and procedural interpretations of logic programs does not apply to Prolog programs, due to the depth-first left-to-right evaluation strategy of Prolog interpreters. We propose a new semantics for Prolog programs based on a new fourvalued logic. The semantics is based on a new concept of completion analogous to Clark's and it enjoys the nice prope...