A Survey of Work on Multiple Valued Logic and its Applications
David Rine
Topics 1-3:
Topic 1.
"Equivalence and Transformations for Post Multivalued Algebras"
Nutter, R.S., Jr. Swartwout, Robert E. ; Rine, David C.
Published in: IEEE Transactions on Computers (Volume:C-23 , Issue: 3 )
Page(s): 294 - 300
ISSN : 0018-9340
DOI: 10.1109/T-C.1974.223925
Date of Publication :
March 1974
Sponsored by : IEEE Computer Society
Publisher: IEEE
Abstract.
Four commonly used multivalued algebras, the disjoint system of Post algebra developed by
Epstein, the monotonic system of algebra called Muehldorf by some authors, the free system of
algebra introduced by Braddock and Epstein, and the Herrmann system of algebra generalized
here from its original three element algebra, are shown to be isomorphic. Transformations are
then developed for transforming from one algebra to another. An example problem is
presented to illustrate transforming from any of the above to the disjoint system of Post
algebra.
INSPEC: NON CONTROLLED INDEXING
Disjoint system of algebra, logic simplification, many-valued logic, multiple-valued switching
functions, multivalued logic, nonbinary logic, Post algebra.
AUTHOR KEYWORDS
1
Disjoint system of algebra, logic simplification, many-valued logic, multiple-valued switching
functions, multivalued logic, nonbinary logic, Post algebra.
IEEE TERMS
Algebra
Computer science
Logic functions
Multivalued logic
Registers
Switching systems
References
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1672518
Showing 1-16 of 16 Results
C.M. Allen and D.C. Givone "A minimization technique for multiple-valued logic systems", IEEE
Trans. Comput., vol. C-17, pp.182 -184 1968
Abstract | Full Text: PDF (544KB)
R. Braddock , G. Epstein and H. Yamanaka "Multiple-valued logic design and applications in
binary computers", Conf. Rec. 1971 Symp. Theory and Applications of Multiple-Valued Logic
Design, pp.13 -25
G. Epstein "The lattice theory of Post algebras", Trans. Amer. Math. Soc., vol. 95, pp.300 -317
1960
[CrossRef]
D.D. Givone and R. W. Snelsire Final report of the design of multiple-valued logic system, 1968
V. Hamacher and Z. Vranesic "Multivalued versus binary high speed multipliers", Conf. Rec.
1971 Symp. Theory and Applications of Multiple-Valued Logic Design, pp.42 -53
R.L. Herrmann "Selection and implementation of a ternary switching algebra", 1968 Spring
Joint Comput. Conf., AFIPS Conf. Proc., vol. 32, pp.283 -290
2
[CrossRef]
C.Y. Lee and W.H. Chen "Several valued combinational switching ing circuits", Trans. Amer.
Inst. Elec. Eng., vol. 75, pp.278 -283 1956
R.S. Nutter and R.E. Swartwout "A ternary logic minimization technique", Conf. Rec. 1971
Symp. Theory and Applications of Multiple-Valued Logic Design, pp.112 -123
R.S. Nutter Function simplification techniques for Postian multi-valued logic systems, 1971
E.L. Post "Introduction to a general theory of elementary propositions", Amer. J. Math., vol.
43, pp.163 -185 1921
[CrossRef]
P.C. Rosenbloom "Post algebras I. postulates and general theory", Amer. J.Math., vol. 64,
pp.167 -188 1942
[CrossRef]
J.R. Shonfield Mathematical Logic, 1967 :Addison-Wesley
T. Traczyk "Axioms and some properties of Post algebras", Coll. Math., vol. 10, pp.193 -209
1963
A.S. Wojcik Relationships between post and boolean algebras with applications to multi-valued
switching theory, 1971
C. Ying and A.K. Susskind "Building blocks and synthesis techniques for the realization of M-ary
combinational switching functions", Conf. Rec. 1971 Symp. Theory and Applications of ultipleValued Logic Design, pp.183 -205
M. Yoeli and G. Rosenfeld "Logical design of ternary switching circuits", IEEE Trans. Electron.
Comput., vol. EC-14, pp.19 -29 1965
Topic 2.
D. Rine, "Computer Science and Multiple-Valued Logic
Theory and Applications"
http://www.sciencedirect.com/science/book/9780720404067
Computer scientists, computer engineers, applied mathematicians, and physicists are familiar
with options in which there are no middle choices between true and false. Statisticians are
familiar with the soft logic of probability, and physicists are familiar with the logic of
3
uncertainty. The lack of such choices is inconvenient and critical when trying to determine
whether the status of a computer system is go, wait, or no-go. Multiple-valued logic is
concerned with these intermediate choices. The major drawback to overcomplicated flowcharts
developed by computer programmers is the difficulty with which they are checked, corrected,
or modified. This situation suggests a structured design approach, where a structured flowchart
or well designed program is built up to an adequate level of detail according to definite rules
from a small, simple, and sufficient set of elemental blocks or primitives. Developments in
multiple-valued logic as related to computer science include a range of disciplines in which
comparisons to multiple-valued logic and computer science are being made, such as neural
science and ethology.
Topic 3.
D. Rine, http://www.computer.org/csdl/mags/co/1974/09/020032.pdf
"The development of multiple valued logic as related to computer science" IEEE Computer, Vol.
7, Issue 9, September 1974. IEEE Computer Society.
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MC.1974.6323304
ABSTRACT
Computer scientists are familiar with options in which there are no middle choices between
true and false. The lack of such choices is inconvenient — even critical — for example, when
determining whether the status of a computer system is go or no-go. Multiple-valued logic is
concerned with these intermediate choices.
Historic Reference.
Nutter, R.S., Jr.; Swartwout, Robert E.; Rine, David C., "Equivalence and Transformations for
Post Multivalued Algebras," Computers, IEEE Transactions on , vol.C-23, no.3, pp.294,300,
March 1974
doi: 10.1109/T-C.1974.223925
Abstract: Four commonly used multivalued algebras, the disjoint system of Post algebra
developed by Epstein, the monotonic system of algebra called Muehldorf by some authors, the
free system of algebra introduced by Braddock and Epstein, and the Herrmann system of
algebra generalized here from its original three element algebra, are shown to be isomorphic.
Transformations are then developed for transforming from one algebra to another. An example
problem is presented to illustrate transforming from any of the above to the disjoint system of
Post algebra.
keywords: {Disjoint system of algebra, logic simplification, many-valued logic, multiple-valued
4
switching functions, multivalued logic, nonbinary logic, Post algebra.;Algebra;Computer
science;Logic functions;Multivalued logic;Registers;Switching systems;Disjoint system of
algebra, logic simplification, many-valued logic, multiple-valued switching functions,
multivalued logic, nonbinary logic, Post algebra.},
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672518&isnumber=35082
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