SUO: Re: Foundations for Ontology
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John,
I would like to begin a careful examination of the role of abductive reasoning
in ontology generation, paradigm shifting, theory change, and things like that.
Let me start with these bits from your paper
on "Signs, Processes, and Language Games":
http://www.jfsowa.com/pubs/signproc.htm
| In analyzing the techniques of logical reasoning, [Peirce] observed that
| deduction exemplifies Firstness because it depends only on the syntax of
| propositions. Induction exemplifies Secondness because it depends on
| a dyadic relation between propositions and reality. In looking for
| the missing third, he discovered the principle of abduction, which
| generates new hypotheses, which are further tested by the techniques
| of deduction and induction. The AI methods of heuristics (which
| Peirce spelled heuretic) are special cases of abduction.
Okay, we both know that wasn't exactly how it happened, as Peirce was already
well-versed in Aristotle's syllogistic description of anagoge, epagoge, apagoge,
long before he transformed the entire scheme into something slightly more general,
but never mind all that now, as I get all the reasons why these "Just So Stories"
have to take on this roughly plausible sort of character.
However, I do think that it would help to start this study back within the context
of its classical and scholastic configurations -- and not just because it's a big
part of my current work to understand how and why Peirce made this transformation --
but more because we can look at the process of inquiry at its most primitive stages,
well within the framework of propositional calculus and simple boolean lattices.
So here is the venerable scheme of terminology,
tacked onto a triangular configuration that we
may treat as embedded within a boolean lattice:
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | A > \
| | \ / \
| Fact | <-¤-D o Y
| | / \ /
| | I > /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 1. Three Kinds of Inference
The terms "Fact", "Rule", "Case" are medieval nicknames for the propositions
that would be called the "conclusion", "major premiss", "minor premiss",
respectively, in the simplest form of deductive syllogism.
Thus, we have the following scheme:
1. Deduction takes a Case, the minor premiss of the form X => Y,
matches it with a Rule, the major premiss of the form Y => Z,
then adverts to a Fact, the bound outcome of the form X => Z.
2. Induction takes a Case of the form X => Y,
matches it with a Fact of the form X => Z,
then adverts to a Rule of the form Y => Z.
3. Abduction takes a Fact of the form X => Z,
matches it with a Rule of the form Y => Z,
then adverts to a Case of the form X => Y.
Even more succinctly:
Table 2. Three Kinds of Inference
o-----------o-----------o-----------o-----------o
| | Abduction | Deduction | Induction |
o-----------o-----------o-----------o-----------o
| Premiss | Fact | Rule | Case |
| Premiss | Rule | Case | Fact |
| Outcome | Case | Fact | Rule |
o-----------o-----------o-----------o-----------o
We can think of these three kinds of inference as three different ways
of moving around in a lattice of concepts, depending on the kinds of
concept-data tensions that are present in a given inquiry situation.
Have to break here ...
Jon Awbrey
| Abduction. Peirce coined the term abduction for the process of generating hypotheses,
| whose consequences are later developed by deduction. The term has been adopted by AI
| researchers for an initial stage of hypothesis formation to be followed by a later
| stage of deduction from the hypotheses. Abduction may be considered a process of
| selecting chunks of knowledge from the soup, evaluating their relevance to the
| problem at hand, and assembling them into a consistent theory. It may be
| performed at various levels of complexity:
|
| Reuse. Do an associative search for a predefined theory
| that can be reused for the current problem.
|
| Revise. Find a theory that approximately matches
| the problem at hand and use belief revision
| techniques to tailor it for the current situation.
|
| Combine. Search for scattered fragments of knowledge
| and perform repeated steps of belief revision
| to combine them into a complete theory.
|
| Abduction and deduction may be used iteratively. Peirce noted
| that after a hypothesis is formed by abduction, its consequences
| must be tested by deduction. If the implications do not match reality,
| the hypothesis must be revised in another stage of abduction. Figure 6.12
| illustrates the use of abduction for extracting a theory or parts of a theory
| from the knowledge soup, belief revision for modifying the theory, and deduction
| for answering questions.
|
| Learning by any agent human, animal, or robot involves a constant cycling
| from data to models to theories and back to a reinterpretation of the old data
| in terms of new models and theories. Beneath it all, there is a real world, which
| the entire community of inquirers learns to approximate through repeated cycles of
| observation, induction, abduction, deduction, and testing.
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