[Fis] The ternary logic. Neutrosophic logic. Bayesian (pattern) logic
Momme von Sydow
momme at von-sydow.de
Thu May 2 20:31:27 CEST 2024
There is an interesting *field of normative modelling and empirical
research at the intersection of logics and probability in psychology and
philosophy as well.* One has to distinguish ternary logics, many-valued
logics, fuzzy logic, quantum probability accounts applied to logical
issues. Particularly interesting, in my view, are some accounts,
adressing apparent deviations from normative probability theory and
logics (like the Conjunction fallacy).
I allow myself to draw your attention to *Bayesian Logic* (or Bayesian
pattern logic), that I have been working on. This is an inductive,
probabilistic logic, concerned with the classical (16 combinatorically
possible) binary logical connectives of propositional logics. It is
based on standard Kolmogorov probabilities, but is concerned with
logical *patterns* (probabilistic analogues of truth tables as a whole).
The logic assigns priors, likelihoods (based on frequency data) and
posteriors to probability tables as wholes. This may sound quite
standard Bayesian, but the results here differ strongly from
(extensional) probabilities which use relative frequencies or subjective
probability measures (based on priors and likelihoods based on relative
frequencies) more directly. Bayesian logics instead provides a kind of
rational re-formulation of intensional (<> intentional) probability. The
'emergent' intensional probability linked to the pattern of a particilar
connector differs substantially from the composing standard extensional
probabilities. In my ideosyncratic view this logic seems to provide a
rational reconstruction for a number of biases discussed in psychology
and philosophy as supposedly irrational. For instance it allows a
logical conjunction A AND B to be more probable than inclusive
disjunction A OR B (or both), which would not be possible using
Kolmorgorov probabilities with logical connectives more directly.
Of course, this parsimonic Bayesian logic, on its normative side, is
required to make assumtions, in particular that random variables are iid
(otherwise it would fall pray to the Humean problem of induction) and it
is only developed and empirically supported (as minority position) as an
inductive logic. It is not jet developed in the traditional core field
of logic, i.e. that of reasoning and drawing inferences. Nonetheless,
perhaps someone wants to have a look at it.
https://urldefense.com/v3/__https://www.researchgate.net/publication/228529771_The_Bayesian_logic_of_frequency-based_conjunction_fallacies__;!!D9dNQwwGXtA!Wkpc6gXEAUa7vTN073irJvmiGFm1M04ePrzamc3puONiLj0j7VhXXNyOKSfhw7vlOZkl9aV2Cf3k1dD6zyBvCQ$
https://urldefense.com/v3/__https://www.researchgate.net/publication/289489883_Towards_a_Pattern-Based_Logic_of_Probability_Judgements_and_Logical_Inclusion_Fallacies__;!!D9dNQwwGXtA!Wkpc6gXEAUa7vTN073irJvmiGFm1M04ePrzamc3puONiLj0j7VhXXNyOKSfhw7vlOZkl9aV2Cf3k1dD4d49YjQ$
https://urldefense.com/v3/__https://www.researchgate.net/publication/316248863_Rational_and_Semi-Rational_Explanations_of_the_Conjunction_Fallacy_A_Polycausal_Approach_Momme_von_Sydow__;!!D9dNQwwGXtA!Wkpc6gXEAUa7vTN073irJvmiGFm1M04ePrzamc3puONiLj0j7VhXXNyOKSfhw7vlOZkl9aV2Cf3k1dC06pUjIw$
https://urldefense.com/v3/__https://www.researchgate.net/publication/326719115_Is_there_a_Monadic_as_well_as_a_Dyadic_Bayesian_Logic_Two_Logics_Explaining_Conjunction_'Fallacies'?_sg*5B0*5D=off0L4Q8oHh8xAUUBUFcPOxlGLfGnPAHbDZSx7Vmtq11m8Z4n2X9-QKquQAnyiRHJX6abs99Qd8X6_IYBEU1YtiNV37Z9OBgNc8O_IhY.-X-5XcXwnj-KbyGiVCkbIQR3ORzC5PNiSdTAiU6-_3V3YIUO5up--0oidXT4bHC1wZVBtQG5bmHHu9eXLuVVbA&_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InB1YmxpY2F0aW9uIiwicGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19__;JSU!!D9dNQwwGXtA!Wkpc6gXEAUa7vTN073irJvmiGFm1M04ePrzamc3puONiLj0j7VhXXNyOKSfhw7vlOZkl9aV2Cf3k1dCt6Ou4RA$
Sorry, don't want to provide Spam, in this mailing list, which I do
value very much. But sometimes - as you know - aspects of the 'TAO'
could be revealed by technicalities ;-)
Best regards Momme
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Dr. Dr. Momme v. Sydow
https://urldefense.com/v3/__http://www.von-sydow.de__;!!D9dNQwwGXtA!Wkpc6gXEAUa7vTN073irJvmiGFm1M04ePrzamc3puONiLj0j7VhXXNyOKSfhw7vlOZkl9aV2Cf3k1dA03k3Mpw$
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Am 02.05.2024 um 17:08 schrieb Stuart Kauffman:
> Lou am I correct that fuzzy logic does not handle quantum uncertainty
> where there are no "facts of the matter" between “measurements”? Stu
>
>> On May 2, 2024, at 9:01 AM, Louis Kauffman <loukau at gmail.com> wrote:
>>
>> Multiple valued logic with values in interval from 0 to 1 allows a
>> continuity of possibilities.
>> To see more of what people have done and are doing with it see the
>> whole literature on fuzzy logic.
>> I would be interested in what you hope to do with such ideas.
>>
>>
>>> On May 2, 2024, at 5:12 AM, Dr. Eric Werner <evwerner at gmail.com> wrote:
>>>
>>> Very nice Louis!
>>> Now can we connect this to AI encodings and inference?
>>> Best,
>>> Eric
>>>
>>> Sent from my iPhone
>>>
>>>> On May 1, 2024, at 23:41, Louis Kauffman <loukau at gmail.com> wrote:
>>>>
>>>> Dear Folks,
>>>> There is a very nice way (not the only way!) to start in multiple
>>>> valued logics by extending from 0 and 1 to all the values between 0
>>>> and 1 in the real numbers.
>>>> This actually was done by Boole. In a modern version I will let ~x
>>>> = 1-x where x is in [0,1] = {x| 0<= x<= 1}. We can let x AND y = x
>>>> ^ y = xy the usual product of numbers.
>>>> Thus 0^0 = 0, 0^1=0, 1^1=1. Then define x v y = ~(~x ^ ~y) to
>>>> preserve the DeMorgan rule.
>>>> Then x v y = ~(~x ^ ~y) = 1 - (1-x)(1-y) = 1-(1-x-y+xy) = x+y - xy.
>>>> (Note that 1 v 1 = 1 + 1 - 1x1 = 1 as desired for Boolean algebra.)
>>>> Then we have Boolean algebra for 0 and 1 and an extension that can
>>>> be thought of as probabilistic for values between
>>>> 0 and 1. Note that ~(1/2) = (1/2) so there is a Third Value that
>>>> sits on the fence. Since this works for 0 and 1, you can write a
>>>> computer program with these formulas and then compute in Boolean by
>>>> taking 0 and 1 values.
>>>> Best,
>>>> Lou
>>>>
>>>>
>>>>> On May 1, 2024, at 1:40 AM, joe.brenner at bluewin.ch wrote:
>>>>>
>>>>> Dear Krassimir,
>>>>>
>>>>> You and others interested in this form of epistemic logic should
>>>>> by all means look at the 3VL neutrosophic logic of the
>>>>> Romanian-American Florentin Smarandache at the U. of New Mexico.
>>>>> It is a highly sophisticated fuzzy intuitionist logic that offers
>>>>> more operators than simple ternary logic.
>>>>>
>>>>> As I discussed with Florentin some ten years ago, there is /no
>>>>> /relation between neutrosophic logics and an ontological logic of
>>>>> processes. They can be applied without reference to it.
>>>>>
>>>>> Best wishes,
>>>>> Joseph
>>>>>
>>>>> ----Message d'origine----
>>>>> De : itheaiss at gmail.com
>>>>> Date : 30/04/2024 - 22:09 (E)
>>>>> À : fis at listas.unizar.es
>>>>> Objet : [Fis] The ternary logic
>>>>>
>>>>> Dear Kate,
>>>>>
>>>>> I want to point out that my note was just one variation of the
>>>>> well-known ternary logic.
>>>>>
>>>>> The ternary logic, or three-valued logic (3VL), is a logic
>>>>> system with three truth values: TRUE, FALSE, and UNKNOWN. It
>>>>> is superior to binary logic, but because of the significantly
>>>>> larger set of 27 unary operators, the engineer who created the
>>>>> first electronic computer (do you know who he was?) preferred
>>>>> the simpler binary (Boolean) logic.
>>>>>
>>>>> Boolean logic allows 2^2 = 4 unary operators; the addition of
>>>>> a third value in ternary logic leads to a total of 3^3 = 27
>>>>> distinct operators on a single input value.
>>>>>
>>>>> At the same time, if we want to achieve development in the
>>>>> field of artificial intelligence and its applications, it is
>>>>> better to use ternary logic. It can be implemented
>>>>> programmatically without much effort, so it is not a question
>>>>> of implementation, but rather of using it expediently.
>>>>>
>>>>> For instance the database structural query language SQL
>>>>> implements ternary logic as a means of handling comparisons
>>>>> with NULL field content. NULL was originally intended to be
>>>>> used as a sentinel value in SQL to represent missing data in a
>>>>> database, i.e. the assumption that an actual value exists, but
>>>>> that the value is not currently recorded in the database. In
>>>>> SQL, the intermediate value is intended to be interpreted as
>>>>> UNKNOWN.
>>>>>
>>>>> In the 3VL logic based on -1,0,1 the intermediate value is 0.
>>>>>
>>>>> Thank you Kate for the very interesting interpretation of
>>>>> intermediate value for the case of emotions!
>>>>>
>>>>>
>>>>> Dear Stu,
>>>>>
>>>>> I would like to touch briefly on the "Hindu Jain concept of
>>>>> Unmanifest, True, Unmanifest, False" you noted.
>>>>>
>>>>> This is not analogous to "I don't know," because "I don't
>>>>> know" means "I have no way of knowing." This is a ternary
>>>>> logic - "Yes", "No" and "Unknown".
>>>>>
>>>>> In my opinion, "Unmanifest, True, Unmanifest, False", is based
>>>>> on the recommendation to perceive reality as "it is" and at
>>>>> the same time as "it is not", qualified with "perhaps", to
>>>>> understand Absolute Reality. This is a variant of binary
>>>>> logic, in probably one of its oldest versions.
>>>>>
>>>>> I will recall that any change in a given entity, as a result
>>>>> of interaction with another (= reflection = data = ontological
>>>>> information), only after being recognized by the Infos (=
>>>>> human = agent = subject) becomes a mental model (= information
>>>>> = data with meaning = knowledge = epistemological information).
>>>>>
>>>>> This is what leads to the confusion of what "information" is,
>>>>> because in everyday life we use the term “information” for
>>>>> both data and knowledge. And in fact, information appears
>>>>> during the transition from data to knowledge, which takes
>>>>> place in the temporary (working) memory of the brain. Data
>>>>> enters it, is recognized, and is perceived as information (the
>>>>> data acquires meaning), after which it is stored in long-term
>>>>> memory. Thus, the temporary memory can be considered as a
>>>>> converter of the data coming at the input into information
>>>>> that is stored in the permanent memory and we usually call
>>>>> "knowledge". The opposite transition from knowledge to data
>>>>> is possible.
>>>>>
>>>>> But the reflection (the data, the ontological information) may
>>>>> not be recognized by the Infos (= human = agent = subject)
>>>>> and, under certain conditions, continue to exist in long-term
>>>>> memory as a reflection without meaning. This is exactly the
>>>>> case with "I don't know". Thus we enter the ternary aspect of
>>>>> consciousness, which is actually the engine of knowledge
>>>>> because it leads to the generation of new mental models.
>>>>>
>>>>> If we make an analogy with Schrödinger's Cat, then in ternary
>>>>> logic the observation can give one of three answers: "The cat
>>>>> is alive", "The cat is dead", "That in the box is not a cat
>>>>> and one cannot recognize what it is"!
>>>>>
>>>>> This suggests that our brain is not quantum, but a vastly more
>>>>> complex system.
>>>>>
>>>>> If we want the Jain concept to become a ternary, then we
>>>>> should have three concepts - "Unmanifest, True", "Unmanifest,
>>>>> False", and "Unmanifest, Unknown ".
>>>>>
>>>>> With respect,
>>>>>
>>>>> Krassimir
>>>>>
>>>>> PS: In the future, possibly it will be interesting to discuss
>>>>> information trialectics philosophy.
>>>>>
>>>>>
>>>>>
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>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
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