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Results for “multi-valued logic”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1979

Plausible inference: A multi-valued logic for problem solving

A new logic is developed which permits continuously variable strength of belief in the truth of assertions. Four inference rules result, with formal logic as a limiting case. Quantification of belief is defined. Propagation of belief to linked assertions results from dependency-based techniques of truth maintenance so that local consistency is achieved or contradiction discovered in problem solving. Rules for combining, confirming, or disconfirming beliefs are given, and several heuristics are suggested that apply to revising already formed beliefs in the light of new evidence. The strength of belief that results in such revisions based on conflicting evidence are a highly subjective phenomenon. Certain quantification rules appear to reflect an orderliness in the subjectivity. Several examples of reasoning by plausible inference are given, including a legal example and one from robot learning. Propagation of belief takes place in directions forbidden in formal logic and this results in conclusions becoming possible for a given set of assertions that are not reachable by formal logic.

Friedman, L.↗
NASA NTRS1991

Canonical multi-valued input Reed-Muller trees and forms

There is recently an increased interest in logic synthesis using EXOR gates. The paper introduces the fundamental concept of Orthogonal Expansion, which generalizes the ring form of the Shannon expansion to the logic with multiple-valued (mv) inputs. Based on this concept we are able to define a family of canonical tree circuits. Such circuits can be considered for binary and multiple-valued input cases. They can be multi-level (trees and DAG's) or flattened to two-level AND-EXOR circuits. Input decoders similar to those used in Sum of Products (SOP) PLA's are used in realizations of multiple-valued input functions. In the case of the binary logic the family of flattened AND-EXOR circuits includes several forms discussed by Davio and Green. For the case of the logic with multiple-valued inputs, the family of the flattened mv AND-EXOR circuits includes three expansions known from literature and two new expansions.

Perkowski, M. A.↗
NASA NTRS1998

Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference

Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.

Walden, Maria A.↗