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On Repairing Reasoning Reversals via Representational Refinements (01)
Alan Bundy, Fiona McNeill and Chris Walton (02)
The Authors seem confused to me. (03)
>However, it is the thesis of this paper that none of this goes
>far enough. In addition, we must consider the dynamic evolution
>of the underlying formalism in which the knowledge is represented.
>
>
That none of it goes far enough leaves me with the impression that the
general direction (towards complex independent
descriptive-representational conceptualizations(??)) is okay, when it
should be what is called up for defense. The second sentence, with the
phrase "we must consider the dynamic evolution of the underlying
formalism in which knowledge is represented" is troubling to me. (04)
What is this "underlying formalism" and how do you know it evolves?
People evolve/are evolving through successive generations. If our
thought processes are so different from the ancient people, from whom we
have evolved, why do our primordial instincts still orient us? How
exactly, have our thinking processes evolved, say, from Aristotle? Given
2500 years, did we evolve? The terms evolve or evolution conjure up
concepts of evolutionary processes of adaptation. Has the syllogism
evolved then; to what extent has it adapted to our personal needs? If
science has evolved, why does western science, and specifically logic or
software engineers, still cling to the scientific methods of the Ancient
Greeks. The concept of change belongs here but the concept of evolution,
imho, obfuscates the nature of the kinds of knowledge we can rely upon. (05)
Personal knowledge is improved and perhaps even repaired and evolving
(changing) --it is clear, but mathematical formalisms that are a matter
of public knowledge are usually timeless and explanatory. Being
timeless, how can they evolve? (06)
Did Newton's formalism's evolve or change when Einstein introduced
relativity? Did Einstein's formalism change Newton's formalism (even
though they are, or conceded to be, incompatible theories)? Did Steven
Hawking change them when he deferred to both to formalize how black
holes sort of boil away and evaporate? (07)
What evolves here? There are no evolutionary processes in these
formalisms. If you want to say that individual and social perceptions
change and knowledge and some beliefs can change -say that, but
attacking mathematical formalism or the motivation to achieve a
mathematical formalism seems misguided. (08)
Maybe Barry Smith can name some radiographic scanning machines or other
medical instruments (any performing computations or memory operations)
that could be or have been invented, without the aid of any stable,
formal, mathematical, scientific model (or measure), but I cannot. (09)
>To be concrete, in a logic-based representation the predicates
>and functions, their arities and their types, may all need to
>change during the course of reasoning.
>
>
>
No doubt. (010)
>Once you start looking, human common-sense reasoning
>is full of examples of this requirement. But such representational
>refinement is not a rare event
>reserved to highly creative individuals; it's a commonplace
>occurrence for all of us. Everyday we form new models to
>describe current situations and solve new problems: from
>making travel plans to understanding relationships with and
>between newly met people. These models undergo constant
>renement as we learn more about the situations and get
>deeper into the problems.
>
> (011)
I cannot say I disagree but I cannot help thinking the authors are
confusing perception with representation, and therefore, perceptual
models (personal, internal) with representational models (public,
external). One of them has been formalized by convention- the other
remains unformalized. (012)
>Consider, for instance, the commonplace experience of
>buying something from a coin-in-the-slot machine. Suppose
>the item to be bought costs £2. Initially, we may believe that
>having £2 in cash is a sufficient precondition for the buying
>action. However, we soon learn to refine that precondition
>to having £2 in coins --? the machine does not take notes.
>When we try to use the coins we have, we must refine further
>to exclude the new 50p coins --? the machine is old and has
>not yet been updated to the new coin. But even some of the,
>apparently legitimate, coins we have are rejected. Perhaps
>they are too worn to be recognised by the machine. Later a
>friend shows us that this machine will also accept some foreign
>coins, which, apparently, it confuses with British ones.
>Rening our preconditions to adapt them to the real world
>of this machine does not just involve a change of belief.
>We have to represent new concepts: ?coins excluding the new
>50p?, ?coins that are not too worn to be accepted by this
>particular machine?, ?foreign coins that will fool this machine?,
>etc.
>
>
>
The claim for a change of belief is not warranted. There is only
confusion of concepts, relations and beliefs.. (013)
I believe that machines that supposedly recognize coins break down and
can even be fooled by none-too-clever people. Even though I could not
articulate this belief then, I have held that belief since a very young
age, when someone showed me how to attach a string to a dime in order to
retrieve it and use it again in a phone booth. It was near the time I
first had the personal requirement to use coin-operated machines. My
perceptions have not changed after more than a half-century of experience. (014)
I think anyone who approaches a coin machine of any kind with the
(lightweight) assumption (in respect to hard belief) that all they need
is any currency equal to the price-- must live on the evening, or is it
the morning, star, and not on earth. Here on earth, even in England I
assume, we learn it is best to have clear instructions and the correct
change in the correct denominations when using coin machines. (015)
Because I think that, does not qualify it as a belief of any kind. (016)
Before I was sixteen years old, I learned that the coke machines in my
town would not accept Canadian coins of the same denomination. Still,
it did not alter my belief about coin-operated machines. I did not have
to learn new concepts. (017)
I had more than the concepts of "Canadian money" and the "coin-operated
coke machine". I had personal experience with these real objects. New
relations, suppositions and perhaps a new pattern resulted from the
experiences I had with them. Otherwise, the experiences added facts to
my memory that supports my belief that machines break down at some point
and cannot be relied upon for perfect and trouble-free operation at all
times. Not to mention the ancillary belief of "correct change". (018)
Perception or situational awareness can turn out wrong and it is useful
to understand the nature of these failures and to have a mechanism to
repair them. I will add that I agree that we must clarify these things
and we should thereby seek models that clarify and explain, rather than
obfuscate, knowledge. (019)
For the semantic web to work for people it must capture what is
significant in the moment, that is, the semantic web must account for
the patterns of (usually natural) entities and elements, (usually
natural) processes, and the relationships between them, in a specific
context served by the semantic web. (020)
To accomplish that we have to refine our collective thoughts and ideas
about the objects and entities of our thoughts and clarify the abstract
categories, objects and functions we use to classify, process and reason
about those objects and entities. (021)
In my opinion the "objects of our thoughts" are not the "abstract
objects" we use for thinking; just as a situational awareness, even an
initial impression, or a conjecture, are not justified true beliefs.
This is a source of great confusion. It is not to say personal
impressions are not supported by some justified true beliefs. (022)
This group might consider the work of the biologist Robert Rosen who
formalized the work of the human metabolism by creating a mathematical
model of metabolic reactions he called (M,R) systems or Metabolic-Repair
systems. Rosen maintained that modeling was the essence of scientific
discovery. (023)
According to Robert Rosen, John Sowa and other scientists, concept
graphs are an essential part of the conceptual building blocks of
meaning and knowledge. Rosen's (M,R) systems owe many of their
properties to graph theory and the 1950s-style blackbox analysis of
electronic circuits, but (more significantly) to an interpretation that
identified an enzyme with a mathematical mapping. (024)
In his view, every metabolic reaction, such as the one catalyzed by the
enzyme glucokinase: Glucose + ATP --> Glucose 6-phosphate + ADP can be
formalized as a1 + a2--> b1 + b2, and can be viewed as the action of a
mapping operator (-->) that transforms molecules a1 and a2 into
metabolites b1 and b2. (025)
On this same basis, every "thought reaction" can be seen as the action
of a catalyst that transforms impinging energies and forces (a1) and
psychophysiolgical impulses (a2) into abstracted objects of thought and
the electro-chemical states of neurological activity (b1) and into the
energy expended on articulation and representation (b2 | e.g., speech,
language, music, cultural art, movies, etc.). In this formalism,
Knowledge (K) appears to be a result of thought reactions catalyzed by
a living person (a thinker of thoughts): K = {a1+a2 --> b1+b2}. (026)
The mapping operator --> catalyzes the thought reaction by transforming
the energy input from an impinging environment and emotional or
physiological impulses into the energy needed to articulate the
sensations and sensibilities and formulate a representation. (027)
The inputs a1 and a2, then, are seen to be the cognitive inputs in this
view of the cognitive process in an individual. The inputs are mapped to
perceptions and articulation on the outputs b1 and b2. Such perceptions
and articulations can be seen to construct and or repair reality (or
assumptions, presumptions and beliefs about it) in the same fashion as
the metabolic repair function is used to create enzymes that convert
sugars into proteins to repair the body. (028)
While the transformation can be conceived as a straight mapping of
inputs onto outputs, we know it to be much more biased (via the
operator) -- even to the extreme. In the case of personal knowledge,
however, we are not repairing the organism and creating enzymes as the
metabolism does. We seem to be acquiring, creating and/or preserving
meaning. (029)
We may be constructing a personal reality, our impressions, and
recognizing patterns, by reaching a semantic state of correspondence,
satisfaction and preservation. Accordingly a 'representational state'
takes place or happens in a coordinated framework within the boundaries
abstract objects of thought. (030)
As Edmund Husserl observed, the boundaries of the objects of thought are
not sides, but rather laws entailing the characteristic necessities and
possibilities of kinds of things. The unity of any particular essence
coheres within that determinate outermost boundary which free
imaginative variations of possible cases must not exceed if they are to
remain cases of this particular kind. Essential unity is a centripetal
force. (031)
Every thought pattern leading to knowing, along with every successive
interpretation of a thought pattern, can be seen as a (regular,
repeating) relationship (emerging, arising, obtaining) between a certain
(perceived) context, the very system of objects and forces occurring
repeatedly in that context, and a certain logico- conceptio-spatial
configuration (within the boundaries of the abstract objects of thought)
which allows the objects and forces at work to resolve themselves. (032)
Change and dynamism are a part of the underlying formalism. (033)
-Ken Ewell (034)
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