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 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.

Attached is supporting material.

Dear David,

I will say, not an alternative but an augmentation and a necessity of efficiency and upgrading performances to include large numbers of possibilities, outcomes and decision making processes, as every thing is nature is not of logical value 0 or 1.   

Good. Yes. I would include in this discussion the large number of applications of fuzzy logic which now appears in hundreds of applications in non-parametric analysis, control systems, estimation theory and so forth. Yes. non-binary logic has also appeared in chips that have been used by IBM and others. Do you have an interest?

Dear David, you got one: yes - from me. Now, let me please say this: fuzzy logic is a particular case -historically and logically speaking- of many-valued logics.

Being as it may be, non-binary logic is increasingly being explored and implemented in computing science and a number of other fields. One safely path I know -and have worked on, to some extent- is bio-inspired computation. Here -f.i. when studying bacteria, or other life-like phenomena-, various non-classical logics are being explored. I know about both many-valued logic, and fuzzy logic -as mentioned- but also about paraconsistent logics. For the time being.

Good! Here are a few more, probably not yet thought about, ideas, within the realm of multiple-valued logics and applications. This is merely to expand the horizons of our discussion. Perhaps you can thing of other less well known areas.

Expanding an MVL Discussion.

1. Possibilty Theory

'Possibility theory: As a means for modeling computer security and protection'

Author: David Rine

Published in:· Proceeding

MVL '78 Proceedings of the eighth international symposium on Multiple-valued logic

Pages 276-286

IEEE Computer Society Press Los Alamitos, CA, USA ©1978

http://dl.acm.org/citation.cfm?id=804220

Abstract. The paper studies correlations between computer security specifications and protection techniques in order to find ways by which architectural features of a computer system corresponding to security specifications may be designed or evaluated. The formal basis of the study begins with two basic models introduced in sections 2.1 and 2.2 of the paper. Study objectives include developing a set of models based on a theory of possibilities for “measuring” strengths and weaknesses of “correlations” between security specifications and protection features.

2. Human Communication and Interactions

'A four-valued logic B(4) of E(9) for modeling human communication'

Rine, D. ; Alnakari, R.

Multiple-Valued Logic, 2000. (ISMVL 2000) Proceedings. 30th IEEE International Symposium on

DOI: 10.1109/ISMVL.2000.848633

Publication Year: 2000 , Page(s): 285 - 290

Abstract.In this paper a four-valued logic on B(4) called Hyawic Form UniLogic is presented. Examples of this UniLogic are given which model problems in the area of human interaction, dialog and communication, i.e., human speech. The four values, or states, are isolated, conflicting, coexisting and unifying, forming a square lattice of B(4), Post Algebra of order 2 with 4 elements, inside a Post Algebra on E(9) of order 3 with 9=3*3 elements. This logic has been used to represent human speech problems and their solutions in college classrooms. This logic is used in different universities, countries and languages including France, Algeria, Egypt and USA. It is used for policy analysis and planning, as well as for academic research in inter-communications analysis. Software packages using this logic are available from the developer Dr. Raiek Alnakari

ISSN : 0195-623X

Print ISBN: 0-7695-0692-5

INSPEC Accession Number: 662338

DOI: 10.1109/ISMVL.2000.848633

Publisher: IEEE

3. Training Fuzzy Compunents

'Training fuzzy logic based software components for reuse'

Chen, J. ; Rine, D.C.

Multiple-Valued Logic, 1997. Proceedings., 1997 27th International Symposium on

DOI: 10.1109/ISMVL.1997.601396

Publication Year: 1997 , Page(s): 189 - 194

Abstract. A training framework of an effective method for off-line training of a class of control software components (for example, for first-order nonlinear feedback control systems) using combinations of three kinds of adaptation algorithms is presented. Each control software component is represented at the abstract level by means of a set of adaptive fuzzy logic (FL) rules and at the concrete level by means of fuzzy membership functions (MBFs). At the concrete representation level adaptation algorithms specified for use in adapting MBFs are: genetic algorithms, neural net algorithms, and Monte Carlo algorithms. We specify effective combinations of these three existing adaptation algorithms to train an erroneous FL rule-based software component in the tracker problem. In the framework, training consists of two phases: testing and adapting. In this paper, only the adapting phase is addressed. For each fault scenario adaptation algorithms and their combinations are used to modify the MBFs of the component. Effectiveness of the adapting phase is determined in terms of flexibility, adaptability, and stability. We perform experiments using a genetic algorithm. Simulation results are discussed

Date of Conference: 28-30 May 1997

Page(s): 189 - 194

Print ISBN: 0-8186-7910-7

INSPEC Accession Number: 5615775

DOI: 10.1109/ISMVL.1997.601396

Publisher: IEEE

You might then perhaps wish to study the works of Professor Nicholas Rescher , logic using the excluded middle...

http://en.wikipedia.org/wiki/Nicholas_Rescher

https://philosophynow.org/issues/47/Philosophical_Reasoning_by_Nicholas_Rescher

http://www.amazon.com/Many-valued-Logic-Nicholas-Rescher/dp/0070518939

http://www.hf.uio.no/ifikk/forskning/publikasjoner/tidsskrifter/njpl/vol3no1/manyval.pdf

http://www.unipune.ac.in/snc/cssh/ipq/english/IPQ/6-10%20volumes/09%2001/PDF/9-1-2.pdf

http://en.wikipedia.org/wiki/Nicholas_Rescher

https://philosophynow.org/issues/47/Philosophical_Reasoning_by_Nicholas_Rescher

http://www.amazon.com/Many-valued-Logic-Nicholas-Rescher/dp/0070518939

http://www.hf.uio.no/ifikk/forskning/publikasjoner/tidsskrifter/njpl/vol3no1/manyval.pdf

Dear David, Thank you very much. Professor Rescher was the director of my first postdoc - working precisely on the issues you mention. (Personally, that was the time when I first got acquainted with non-classical logics.

• Congratulations. I had a chance to meet Nicholas a few times while he as at Pittsburgh along with a few other Pitt faculty. Good times! What have been your interests since then?

Maybe one can mention here quantum computing. The spin has a continuous spectrum of orientations - so apparently an infinity of "truth values" - but one chooses two orthogonal directions, calls them "qubits" 0 and 1, and works with them statistically: if most qubits are oriented around 1, the answer is 1, etc... Theoretically, one can choose three spin directions instead of two, but I don't know how sure and reliable does remain the computation. One can however think at disigning the 3-valued quantum gates...

Dear Profs.

Theoretically, the optimal basis for information coding is the exponent (e=2.71828...). Actually, the real basis used in the computer science is 2 (binary Logic). But the nearest basis to the optimum is 3. Technologically, the ternary logic will be the best suitable logic to design efficient computer components.

Can we see in the future the ternary logic circuits for memories and all the components of the computer.

The basical ternary logic functions are well studied in the literature. what is looked for now is the electronic components to design processors, memories and other computer components. Can any one working in this domain propose some technical documents and materials?

Some of the early circuits work started with the Russian SETUN. However, circuits based upon 4, 8 and 16 proved to be more stable and easier to interact with 2 valued circuits. However a bit later a few of my colleagues built emulators based upon the 3 values you mention.

Thank you very much Pr David;

the document is very instructive;

An ieneresting technological solution to design and  set up  ternary computers is to start from the basic logic gates and arithmetic circuits. 

Some interesting transistors based on carbon nanotubes may be the fundamental cells to  elaborate multiple valued logic.

I found the paper of Sheng Lin et al on IEEE Trans on Nanotechnology Vol.10. N°.2 March 2011 "CNTFET-Based Design of Ternary Logic Gates and Arithmetic Circuits" very important in this field.

Can you suggest some goo reasons why ternary logics have not made it into the circuits manufacturing marketplace? Consider issues such as stability, integrability, compatibility, and technology readiness for example. I would be interested in your thoughts.

The ternary logics components are on manufacturing;

Attached papers gave the technological process of these components.