Extending a theory of proof vs. unfounded, quality vs. property,
opp / opp, and system / n-operator, valid vs. incompetent logics.
The following is designed for a simple computer program. The
most complex aspect is if you want to make the process flow
better, by cataloguing all the opposites in the English language
with opposite matching, so that the matching is done

1A. Is what you are considering a paradox?

{1 term: Not a paradox!

2 terms: If opposite terms: you've come to the end of knowledge!

3 terms: Exceptional paradox!

4 terms: If your terms are terms are all opposites, the answer can
be absolute! If your opposite terms are in opposite positions, your
problem can be stated as absolute knowledge.}

General method of Paroxysm

What is a term necessary for the problem?

Do you want to add / delete any terms?

Then the solution to paradox with terms (x, y, z ....) is the
paroxysm with terms (opp x, opp y, opp z...)

Does this answer the problem?

If Y, then:

Do you want to save the solution?

1B. Is what you are considering a problem?

Do you want a general solution?

--> What is the problem?

[One word answer --> Can you be more specific (restate if

-->The ultimate solution to 'X Problem' is 'Opp X solution' which
is short for 'a solution to Opp X'.

Was that helpful?

If no, how about a solution to Opp X? [Skip to frequent answers].

2A. Do you want help with an existing solution?

What are the two best terms of the solution? (x, y)

Is it X? No, then Y.

Is it Y? No, then X.

If it is neither, then you have a paradox [Go to Paradoxes].

If it is X and Y:

"Then you may have a problem".

Do any of the terms serve as solutions?

Yes? Then apply them!

No? Then, do you want a general solution? (above).

3A. Do you have a philosophical problem?

-->Then pick two pairs of opposites that refer to your problem.

-->Which word of the four is most important? (-->A)

-->Then quality A (B) as related to quality C (D) AND / OR
quality A (D) as related to quality C (B) will constitute knowledge
on the subject.

4A. Do you have a systems question?

Neutral, balanced, infinite --> Coherent.
Neutral, balanced, finite --> Modular.
Neutral, imbalanced, infinite --> Essence, History.
Neutral, imbalanced, finite --> Insight.
Asymmetric, balanced, infinite --> Degeneration.
Asymmetric, balanced, finite --> Functions.
Asymmetric, imbalanced, infinite --> Form.
Asymmetric, imbalanced, finite --> Observations.

The above is also available as an academic article at: Seeking comments
and implementation for Javascript.

Further information on coherency theory may be found at:
Logic of Coherence. And elsewhere on the Main Systems Theory



Arbitrary / Paroxysmal Deduction ('Just' Deduction):

A then D
D then A
(A and D are opposites)

'AB' is 'CD'
'BC' is 'DA'
'CD' is 'AB'
'DA' is 'BC'
Basically two deductions.
A and C are opposite, B and D are opposite.
similar to categorical deduction or
two-part paroxysm.

'ABC' is 'DEF'
'BCD' is 'EFA'
'CDE' is 'FAB'
'DEF' is 'ABC'
'EFA' is 'BCD'
'FAB' is 'CDE'
Basically three deductions.
A and D are opposite.
B and E are opposite.
C and F aare opposite.

'A conj B boolean* C conj D' OR
'A conj D boolean* C conj B'
the statement is justice of / just as:
'opp A conj opp B Opp boolean** opp C conj opp D' OR
'opp A conj opp D Opp boolean** opp C conj  opp B'
Basically four deductions.
(The opposites can be nouns or adjective forms.
C must be the opposite of A,
and D must be the opposite of B).
*(for example, 'and' / 'or' / 'always' / 'never'
'rarely' / 'usually')
*(for example, 'or' / 'and' / 'never' / 'always' /
'usually' / 'rarely')
Opp Boolean must be opposite of Boolean in this case,
so the Boolean operators cannot be neutral.

Standard Categorical Deduction:
'A conj B Neutral Boolean* C conj D'
'A conj D Neutral Boolean* C conj B'
Two deductions strictly in terms of A.
Preference is given to the first and second terms.
Otherwise determined.
The second terms retain the same logic regardless of preference.
A and C are opposite.
B and D are opposite.
Conjunction of terms is primary.
*(for example 'is' , 'as is' , 'just as' , 'when' , 'so', 'and as such' )

problem 'ABC...' --> solution 'oppA oppB oppC...'
similar to 3-part deduction, except quantity of terms is explicitly
again, accepts noun or adjective terms.
in this case, conjunction of terms is secondary.

Deduction Using Unconventional Opposites
complexity/perfection/arbitration/ambiguity A --->
perfection/complexity/ambiguity/arbitration opposite A
This is a hand-holding version of categorical deduction
in which specific less common comparisons are preferred
for half of the deduction.
E.g. A is equivalent here to B in standard deductions.
Opposite A is equivalent to D in standard deductions.
A selection is made between A and C, so B and D need
not be selected again.