Critical Decision Making Mechanism
based on Quaternary Logic
Contents
- Vagueness
in Binary thinking
- Quaternary
logic
- Research Objectives & Methodology
- Symbolic Representation of Quaternary values
- Conditions to make a critical decision
- Critical decision making mechanism
Vagueness in Binary thinking
Multi-valued logics and
fuzzy logic have been considered better alternatives to bivalent systems for
handling vagueness. Truth (and falsity) in fuzzy logic, for example, comes in
varying degrees. Consider the following statement.
The apple on
the desk is red.
Upon observation, the apple is a pale shade of red. We
might say it is "50% red". This could be rephrased: it is 50% true
that the apple is red. Therefore, P is 50% true, and 50% false. Now consider:
The apple on
the desk is red and it is not red.
In other words, P and not-P. This violates the law of
noncontradiction and, by extension, bivalence. However, this is only a partial
rejection of these laws because P is only partially true. If P were 100% true,
not-P would be 100% false, and there is no contradiction because P and not-P no
longer holds.
However, the law of the excluded middle is retained,
because P and not-P implies P or not-P, since "or" is inclusive. The
only two cases where P and not-P is false (when P is 100% true or false) are
the same cases considered by two-valued logic, and the same rules apply.
Of course, it may be stated that bivalence must always be
true, and that multi-valued logic is simply by definition a vague state of
perception. That is, multi-valued logic is a convenient way of saying, "This
instance has not been observed in enough detail to determine the truth value of
P." In other words, if a pale apple is 50% red (where red is noted as
P), then P can be said to be 100% true, noting that bivalence makes little
delineation as to the nature of not-P aside from the given, meaning that the
apple might very well be 50% white as well (when white is noted as not-P),
meaning that P and not-P can both be true, but in separate instances, as they
both exist as separate colours, which combine in a larger instance set in
perhaps an unobservable, exceedingly subtle way to create the shade of pale
red. In this case, the apple might be set S, which consisted of P and not-P to
greater or lesser or equal respective degrees, as long as it is acknowledged
that P and not-P are separate instances within a set instance. In this way,
bivalence simply states that white cannot be red, and makes no claim about the
colour of the set instance, to which is applied multi-value logic, in which
case multi-value logic is simply derivative of bivalence as well.
This logic system shows four possible out comes for the event .It does not consider events on dichotomously. The quaternary logic system considers another two out comes which are neglected by the binary logic. The quaternary logic2 provides four logical alternatives concerning any event as follows: A, not-A, A and not-A, neither A nor not-A. It will be argued that these reflect a progressive complexification of understanding to whatever event they are applied.
Applied to any exercise, it is proposed to: start with the constraints of the text (A); to ignore those constraints, treating the text metaphorically, in search of a patterning principle (not-A); to endeavor to fit the pattern to the text with any necessary adjustments (A and not-A); and then to explore the insights implied by that result, reaffirming the pattern, but unconstrained by the limitations of the particular representation (neither A nor not-A).
Aristotelian
Logic Vs Nirvanic views
As noted above a number of 4-fold sub-sets (whether or not part of a larger sub-set) are explicitly structured in terms of: A, not-A, A and not-A, neither A nor not-A. As noted, these suggest a progressive complexification beyond the constraints of Aristotelian logic, which remain, however, a sub-set of the sequence. This implies a progressively increasing challenge to comprehension, suggesting that the more "nirvanic" views might be based on elements of the pattern governed by "neither A nor not-A" (as implied by the phrase "not this, not that", traditionally associated with that state). Correspondingly, the least nirvanic views might be based on elements of the pattern governed by "A".
Quaternary
logical concept on early Buddhism
An intriguing point of departure is a classic Buddhist text entitled the "Brahmajala Sutta" (The Discourse on the All-Embracing Net of Views). This appears to be unique in endeavouring to map out as a system the complete set of fundamental viewpoints. It is the first sutta in the entire collection of the Buddha's discourses in the Pali Tipitaka. Its importance stems from its primary objective, namely the exposition of a scheme of 62 cases designed to include all possible views (past and future) on the central concern of speculative thought, the nature of the self in relation to the world.
This teaching reflects insights formulated 2,500 years ago. It is not the intention to be strictly faithful to it. Rather the intention is to be guided by a method which is based on a fundamental patterning principle in the text itself. The logic of that pattern is to a high degree tetra-Iemmic in the sense that it provides for four logical alternatives concerning any thesis: A, not-A, A and not-A, neither A nor not-A. It will be argued that these reflect a progressive complexification of understanding to whatever domain they are applied. Applied to this exercise, it is proposed to: start with the constraints of the text (A); to ignore those constraints, treating the text metaphorically, in search of a patterning principle (not-A); to endeavour to fit the pattern to the text with any necessary adjustments (A and not-A); and then to explore the insights implied by that result, reaffirming the pattern, but unconstrained by the limitations of the particular
representation (neither A nor not-A).
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Research Objectives & Methodology
Objectives
· To develop a symbolic representation for Quaternary values.
· To apply quaternary values for Critical decision making..
· To designing a quaternary a logic circuit
Methodology
Quaternary and binary values for a event
In the binary Logic
Two values
1. A
2. not A
In the quaternary
Logic
Four values
1. A
2. Both A and not A
3. Neither A nor not A
4. not A
Symbolic
representation of Quaternary values
For the event A, there are the four values (P,Q,R,S). In order of Quaternary logical concept the Critical values of event A are Q and P. After the analyzing the event A and considering exact dichotomy connections are as follows.
|
|
X |
Y |
Z |
= |
XYZ |
|
S |
1 |
1 |
1 |
= |
111 |
|
R |
0 |
1 |
1 |
= |
011 |
|
Q |
0 |
1 |
0 |
= |
010 |
|
P |
0 |
0 |
0 |
= |
000 |
Conditions to make a critical decision
|
immediate after the 0 situation |
X |
|
immediate before the 1 situation |
Y |
|
actual 1 situation |
Z |
These three conditions can be expressed in the binary format. Out put of these values perform a "digital symbol" of relevant quaternary representation. Critical events on the quaternary logic are based on dichotomous values. [ie: 0 (not A) and 1(A)]. Because of the range of this critical events are in between them.
For a any event its sequence order of XYZ gives quaternary values of that event.
If all the out comes give 1 it's quaternary representation is 1
If all the out comes give 0 it's quaternary representation is 0
If two out comes give 1, and other gives 0 it's quaternary representation is both 1 and 0
If two out comes give 0, and other gives 1 it's quaternary representation is neither 1 nor 0
So,
P = 000 in binary = 0 in Quaternary
Q= 100 in binary = neither 1 nor 0 in Quaternary
R= 011 in binary = 1 but 0 in Quaternary
S= III in binary = 1 in Quaternary
For the case A
X- immediate after the not A situation
Y - immediate before the A situation.
Z - actual a situation
P= 000 in binary = Not A
Q= 100 in binary = neither A nor not A
R= 011 in binary = A and not A
S= 111 in binary =A
Critical Decision Making Mechanism
Case
Event identification
Conditional Test
Encoding to binary
Decoding to quaternary