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• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 4|Part 4]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 4|Part 4]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5|Part 5]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5|Part 5]]
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• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
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• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
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• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 8|Part 8]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
 
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
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<p>Tell me where is fancy bred,<br>
 
<p>Tell me where is fancy bred,<br>
 
Or in the heart, or in the head?<br>
 
Or in the heart, or in the head?<br>
−
How begot, how nourished?<br>
+
How begot, how nourishèd?<br>
 
&hellip;<br>
 
&hellip;<br>
 
It is engendered in the eyes,<br>
 
It is engendered in the eyes,<br>
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====4.2.4. The Trivializing of Integration====
 
====4.2.4. The Trivializing of Integration====
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The roots of this "modern" structure appear to be traceable to Aristotle and Descartes.
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The presence of this assumption can be detected in three fundamental texts, the implications of which are well worth the time to examine.
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The first passage occurs in Aristotle's treatise ''On Interpretation'', where he articulates his understanding of the fundamental relationship that exists among objects or objectives in the world, signs and images in the various media of communication, and ideas or "affective impressions" in the mind.  Due to the complexity of this relationship, Aristotle is forced to make a number of simplifying assumptions.  This is a reasonable way to begin, but the fixing of these assumptions into the form of a dogma led many subsequent generations of thinkers to ignore the full potential of this relationship.
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<p>Words spoken are symbols or signs (''symbola'') of affections or impressions (''pathemata'') of the soul (''psyche'');  written words are the signs of words spoken.  As writing, so also is speech not the same for all races of men.  But the mental affections themselves, of which these words are primarily signs (''semeia''), are the same for the whole of mankind, as are also the objects (''pragmata'') of which those affections are representations or likenesses, images, copies (''homoiomata'').</p>
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| align="right" | (Aristotle, ''On Interpretation'', i.16<sup>a</sup>4&ndash;9, p. 115)
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|}
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Aristotle's account contains two claims of constancy or uniformity, asserting that objects and ideas are the same, respectively, for all human interpreters.  This ignores the plurality and the mutability of interpretation, issues that we cannot afford to trivialize in the general consideration of diverse perspectives, if only with respect to the human potential for creative variation, or else in the application to education, where the whole idea is to learn new interpretations.  In their effects, these assumptions lead to the idea that every diversity among observers is merely a disagreement about words.
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The second passage occurs in Aristotle's discussion of psychology, where he argues that the mind has an inherent capacity to integrate the data of the senses.  Aristotle's doctrine of the common sense faculty, or ''sensus communis'', is ably summarized by W.S. Hett in his introduction to Aristotle's treatise ''On the Soul'', where he glosses this term in the following way:
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<p>Book III is chiefly concerned with other vital faculties, but some accessories to the theory of sensation overflow into its opening chapters.  The connecting link is formed by the problem:  What is it that unifies (or distinguishes) the data of sense?</p>
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<p>''Sensus Communis''.  The solution given is that there is a common sense faculty (located in or near the heart &hellip;) which receives and co ordinates the stimuli passed on to it from the various sense organs.  This same faculty also directly perceives the "common sensibles" (''i.e.'', those attributes, such as shape, size, number, etc., which are perceptible by more than one sense), among which Aristotle includes movement and time &hellip;.  It also accounts for our consciousness of sensation, and it is responsible for the process of imagination.</p>
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|-
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| align="right" | (Hett, in (Aristotle, 1936), p. 5)
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|}
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Without trying to answer Shakespeare's question, that appears to be an echo of this very issue, I can stop to make the following observations.  The question of a common sense, that compares and contrasts the data of the senses, can be put in relation to the question of interpretation by recognizing that the data of the senses are particular kinds of signs that naturally refer to objects in the world.
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The third passage that I offer for examination comes from Descartes' ''Discourse on the Method of Properly Conducting One's Reason and of Seeking the Truth in the Sciences''.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>Good sense is the most evenly shared thing in the world, for each of us thinks he is so well endowed with it that even those who are the hardest to please in all other respects are not in the habit of wanting more than they have.  It is unlikely that everyone is mistaken in this.  It indicates rather that the capacity to judge correctly and to distinguish the true from the false, which is properly what one calls common sense or reason, is naturally equal in all men, and consequently that the diversity of our opinions does not spring from some of us being more able to reason than others, but only from our conducting our thoughts along different lines and not examining the same things.</p>
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<p>&hellip;</p>
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<p>As far as reason or good sense is concerned, &hellip; I am ready to believe that it is complete and entire in each one of us, &hellip; that there are degrees only between ''accidents'' and not between the ''forms'' or ''natures'' of the ''individuals'' of a given ''specie''.</p>
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|-
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| align="right" | (Descartes, 1968, 27 28)
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|}
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Surprisingly enough, for all the passage of time that intervenes between the two accounts, and for all the other contingencies that are commonly imagined to have changed, this passage closely echoes in all of its main respects the doctrine of Aristotle concerning the common sense.
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In contemplating these texts and trying to assess their impact on the contemporary scene, one can view them as expressions of underlying assumptions, maintaining their force in our culture whether or not individual members of the culture have ever heard them rendered explicit in precisely these terms before.  These ideas form the basis for an especially refractory modernist thesis, one that I am calling the "triviality of integration".  This is the idea that nothing is lost in taking things apart, as in the processes of a selective observation or a reductive analysis, because "just about anyone" can put things back together.  In other words, common sense suffices to achieve the necessary synthesis or the subsequent reconstruction.
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Aristotle's thesis that the senses are integrated by a common sense has served as a metaphor for the relation of the special sciences to the overall unity of science and it has informed the relations that are instituted between the specialized disciplines and the whole realm of knowledge that is presided over by the university.  In exploiting this template, it has been taken for granted that the disciplines bear the same automatic relationship to the whole of knowledge that the senses bear to common sense.  This underlying belief leads to the problematic assumption that the integration of the disciplines is a trivial matter.  If anyone can do it, then it is not incumbent on us as educators to develop this skill in our students, and experts in any discipline are automatically well equipped to interpret and synthesize the knowledge that is delivered to them by disciplines in which they are novices.
    
====4.2.5. Tensions in the Field of Observation====
 
====4.2.5. Tensions in the Field of Observation====
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Two kinds of tension in the field of observation were recognized to arise from the pressure toward articulate and analytic description.  There is a tension between the informal context and the formal context and there are tensions that develop as a consequence among the various formal arenas.
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Properly considered, each of these tensions ought to be recognized as a positive force.  Each one serves as a nagging reminder that something important has been omitted from our descriptions, and a sensitivity to the directions of their tugging and nudging can act to draw us back toward wholeness.
    
====4.2.6. Problems of Representation and Communication====
 
====4.2.6. Problems of Representation and Communication====
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Another pair of closely linked issues were seen to arise from the assumption that integration is trivial.  One is the problematic of communications that is created by differing styles of mental models, in other words, by the tendency to form internally coherent but externally disparate systems of mental images.  The other is the disjunction that this axiom permits to occur between the denotative aspects and the connotative aspects in the full representation of reality.  Those who specialize in either aspect tend to ignore the importance of the other, and even if they do appreciate that both are necessary they tend to take the union for granted, rather than recognizing the complex nature of the complementarities and the dualities that are actually involved.
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Aristotle's assumption that objects and their mental impressions are the same for everybody and that only their signs are different for different language communities makes it seem like all problems of communication reduce to problems of translation rather than constituting appreciably different ways of perceiving and interpreting the world.
    
===4.3. The Conduct of Inquiry===
 
===4.3. The Conduct of Inquiry===
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In this section I lay out the pragmatic theory of inquiry that I will use in my study of inquiry driven systems.  In the first section I introduce the basic features of a canonical model of inquiry processes.  After this, I outline two different approaches to the functional structure of inquiry.  Finally, I discuss a collection of computational routines that I have implemented to study various aspects of this model.
    
====4.3.1. Introduction====
 
====4.3.1. Introduction====
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The pragmatic theory or model of inquiry was extracted by C.S. Peirce from basic materials in classical logic and refined in parallel with the historical development of symbolic logic to address problems about the nature of scientific reasoning.  Borrowing on concepts from Aristotle, Peirce identified three fundamental modes of reasoning, called deductive, inductive, and abductive inference.  In rough terms, "abduction" is what one uses to generate a likely hypothesis or initial diagnosis in response to a phenomenon or a problem of interest, while "deduction" is used to clarify and derive relevant consequences of one's hypotheses, and where "induction" is used to test the sum of one's predictions against the sum of the data that is gleaned from experience.  Generally speaking, these three processes operate in a cyclic fashion, systematically reducing the uncertainties and the difficulties which initiate inquiry, and thereby leading to an increase in knowledge.
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In the pragmatic way of thinking everything has a purpose, and the purpose of each thing is the first thing we should try to note about it.  The purpose of inquiry is to reduce doubt and lead to a state of belief, which a person in that state will usually call knowledge or certainty.  As they contribute to the purpose of inquiry, we should appreciate that the three kinds of inference form a cycle that can only be understood as a whole, and none of them makes complete sense in isolation from the others.  For instance, the purpose of abduction is to generate guesses of a kind that deduction can explicate and induction can evaluate.  This places a mild but meaningful constraint on the production of hypotheses, since it is not just any wild guess at explanation that submits itself to reason and bows out when defeated in a match with reality.  In a similar fashion, each of the other types of inference realizes its purpose only in accord with its role in the cycle of inquiry.  No matter how much it may be necessary to study these processes in abstraction from each other, the integrity of inquiry places strong limitations on the effective modularity of its components.
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For our present purposes, the first feature to note in distinguishing these modes of reasoning is whether they are exact or approximate in character.  Deduction is the only type of reasoning that can be made exact, always deriving true conclusions from true premisses, while induction and abduction are unavoidably approximate in their mode of operation, involving elements of fallible judgment and inescapable error in their application.  The reason for this is that deduction, in the ideal limit, can be rendered a purely internal process of the reasoning agent, while the other two modes of reasoning essentially demand a constant interaction with the outside world, a source of phenomena that will no doubt keep exceeding any finite resource, human or machine.  Embedded in this larger reality, approximations can only be judged appropriate in relation to a context of use and a purpose in view.
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A parallel distinction made in this connection is to call deduction a demonstrative inference, while abduction and induction are classed as non demonstrative forms of reasoning.  Strictly speaking, the latter types of reasoning are not properly called inferences at all.  They are more like controlled associations of words or ideas that just happen to be successful often enough to be preserved.  But non demonstrative ways of thinking are inherently subject to error, and must be checked out in practice.
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In classical terminology, forms of judgment that require attention to context and purpose are said to involve elements of art, as compared with science, and rhetoric, as contrasted with logic.  In a figurative sense, this means that only deductive logic can be reduced to an exact science, while the practice of empirical science will always remain to some degree an art.  This fact has important implications for any attempt to support inquiry with automated procedures, constraining both the manner and degree of likely success.  It means that inquiry software will need to be highly interactive, sensitive to run time conditions at two kinds of interfaces, those with its human users and those with the real world.  Further, it means that the main effect of automation will be to speed up and strengthen deductive reasoning.  The chief assistance that computation provides to induction is through measures of fit between theoretical constructs and empirical data sets.  The limited guidance that formal methods can bring to hypothesis generation is restricted to checking the partly logical property of falsifiability and speeding up the subsequent evaluation process.  However, because inquiry is an iterative cycle, improving the rate of performance at any bottleneck can serve to accelerate the entire process.
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As far as automating induction goes, we should not expect a program to make up the data for us, no matter how sophisticated it gets!  Inductive tests can provide measures of how well a theoretical construct fits a set of data, but no fit is perfect, or intended to be.  An inductive concept is supposed to present a simplification of a complex reality, otherwise it would serve no function over and above just staring at the data.  In gauging the slippage between concept and data, the degree of tolerance acceptable in a given situation is a matter of discretionary judgments that have to be made under field conditions.
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When it comes to automating abductive reasoning, we should observe the historical circumstance that it is often the most "unlikely" set of hypotheses that turn out to form the correct conceptual framework, at least when that likelihood has been judged from the standpoint of the previous framework.  Aside from their responsibilities to the inquiry process, abductive hypotheses can be freely generated in the most creative manner possible.  Breaking the mind-set of the problem as stated and reformulating data descriptions from new perspectives are just some of the allowable strategies that are required for success.
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Abductive reasoning is the mode of operation which is involved in shifting from one paradigm to another.  In order to reduce the overall tension of uncertainty in a knowledge base, it is often necessary to restructure our perspective on the data in radical ways, to change the channel that parcels out information to us.  But the true value of a new paradigm is typically not appreciated from the standpoint of another model, that is, not until it has had time to reorganize the knowledge base in ways that demonstrate clear advantages to the community of inquiry concerned.
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The preceding survey has introduced a model of inquiry and charted a series of limits on the automation of inquiry.  We should not be too discouraged by the acknowledgement of these limits.  But we ought to notice that these constraints are not so much limits on the computational extension of human inquiry as they are limits on the instrumental nature of inquiry itself, being the specific adaptation of a finite creature to an infinite world.  In other words, these are only the familiar limits of the scientific method.  They are the limits that make it a method.
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I now return to discussing the pragmatic theory of inquiry, treating its positive features in more depth.  I will examine the theory in terms of a canonical model that illustates generic aspects of inquiry processes.  My plan for the remainder of this section is to introduce basic terminology and issues.
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Inquiry is a form of reasoning process, and therefore a manner of thinking.  Pragmatist philosophers hold that all thought takes place in "signs", which is the word they use for the most general class of signals, messages, symbolic expressions, etc. that might be imagined.  Even ideas and concepts are held to be a special class of signs, namely, internal states of the thinking agent that result from the interpretation of external signs.  The subsumption of inquiry within reasoning and of thinking within sign processes allows us to approach the subject of inquiry from two perspectives.  The "syllogistic approach" views inquiry as a logical species.  The "sign-theoretic" approach views inquiry within a more general setting of sign processes.
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The best point of departure I know for both approaches to inquiry is the following story of inquiry activities in everyday life, as told by John Dewey.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>A man is walking on a warm day.  The sky was clear the last time he observed it;  but presently he notes, while occupied primarily with other things, that the air is cooler.  It occurs to him that it is probably going to rain;  looking up, he sees a dark cloud between him and the sun, and he then quickens his steps.  What, if anything, in such a situation can be called thought?  Neither the act of walking nor the noting of the cold is a thought.  Walking is one direction of activity;  looking and noting are other modes of activity.  The likelihood that it will rain is, however, something ''suggested''.  The pedestrian ''feels'' the cold;  he ''thinks of'' clouds and a coming shower. (Dewey, 1910, 6&ndash;7)</p>
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|}
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I now proceed to analyze this example from the standpoints of the syllogistic and sign-theoretic approaches.  The ultimate task before us is to understand the relation between these two perspectives as they are unified in a single, coherent subject.
    
====4.3.2. The Types of Reasoning====
 
====4.3.2. The Types of Reasoning====
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In this section I discuss the syllogistic approach to inquiry, considering it only so far as the propositional or sentential aspects of the reasoning process are concerned.
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Case, Fact, Rule
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In its original usage a statement of Fact has to do with a deed done or a record made, that is, a type of event that is openly observable and not riddled with speculation as to its very occurrence.  In contrast, a statement of Case may refer to a hidden or a hypothetical cause, that is, a type of event that is not immediately observable to all concerned.  Obviously, the distinction is a rough one and the question of which mode applies can depend on the points of view that different observers adopt over time.  Finally, a statement of Rule is called that because it states a regularity or a regulation that governs a situation, not because of its syntactic form.  At present, all three constraints are expressed in the form of conditional propositions, but this is not a fixed requirement.  In practice, the different modes of statement are distinguished by the roles they play within an argument, not by their style of expression.  When the time comes to branch out from the syllogistic framework, we will find that propositional constraints can be discovered and represented in arbitrary syntactic forms.
    
=====4.3.2.1. Deduction=====
 
=====4.3.2.1. Deduction=====
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In the case of propositional logic, deduction comes down to applications of the transitive law for conditional implications.  Employing a few "terms of art" from classical logic that are still useful in treating these kinds of problems, deduction takes a Case, the minor premiss <math>X \Rightarrow Y,</math> and combines it with a Rule, the major premiss <math>Y \Rightarrow Z,</math> to arrive at a Fact, the demonstrative conclusion <math>X \Rightarrow Z.</math>
    
=====4.3.2.2. Induction=====
 
=====4.3.2.2. Induction=====
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Contrasted with this pattern, induction takes a Fact of the form <math>X \Rightarrow Z</math> and matches it with a Case of the form <math>X \Rightarrow Y</math> to guess that a Rule is possibly in play, one of the form <math>Y \Rightarrow Z.</math>
    
=====4.3.2.3. Abduction=====
 
=====4.3.2.3. Abduction=====
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Cast on the same template, abduction takes a Fact of the form <math>X \Rightarrow Z</math> and matches it with a Rule of the form <math>Y \Rightarrow Z</math> to guess that a Case is presently in view, one of the form <math>X \Rightarrow Y.</math>
    
====4.3.3. Hybrid Types of Inference====
 
====4.3.3. Hybrid Types of Inference====
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In the normal course of inquiry, the fundamental types of inference proceed in the order:  abduction, deduction, induction.  However, the same building blocks can be assembled in other ways to yield different kinds of complex inferences.  Of particular importance for our purposes, reasoning by analogy can be analyzed as a combination of induction and deduction, in other words, as the abstraction and application of a rule.  Because a complicated pattern of analogical inference will be used in our example of a complete inquiry, it will help to prepare the ground if we first stop to consider an example of analogy in its simplest form.
    
=====4.3.3.1. Analogy=====
 
=====4.3.3.1. Analogy=====
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The classic description of analogy in the syllogistic frame comes from Aristotle, who called this form of inference by the name &ldquo;paradeigma&rdquo;, that is, reasoning by example or by a parallel comparison of cases.
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<p>We have an Example (''paradeigma'', or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.</p>
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Aristotle illustrates this pattern of argument with the following sample of reasoning.  The setting is a discussion, taking place in Athens, on the issue of going to war with Thebes.  It is apparently accepted that a war between Thebes and Phocis is or was a bad thing, perhaps from the objectivity lent by non involvement or perhaps as a lesson of history.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>E.g., let A be "bad", B "to make war on neighbors", C "Athens against Thebes", and D "Thebes against Phocis".  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.</p>
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| align="right" | (Aristotle, ''Prior Analytics'', 2.24)
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|}
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We may analyze this argument as follows.  First, a Rule is induced from the consideration of a similar Case and a relevant Fact.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>D \Rightarrow B,</math>
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| width="60%" | "Thebes vs Phocis is war against neighbors".
 +
| width="20%" | (Case)
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|-
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| <math>D \Rightarrow A,</math>
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| "Thebes vs Phocis is bad".
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| (Fact)
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|-
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| <math>B \Rightarrow A,</math>
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| "War against neighbors is bad".
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| (Rule)
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|}
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Next, the Fact to be proved is deduced from the application of this Rule to the present Case.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>C \Rightarrow B,</math>
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| width="60%" | "Athens vs Thebes is war against neighbors".
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| width="20%" | (Case)
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|-
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| <math>B \Rightarrow A,</math>
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| "War against neighbors is bad".
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| (Rule)
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|-
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| <math>C \Rightarrow A,</math>
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| "Athens vs Thebes is bad".
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| (Fact)
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|}
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In practice, of course, it would probably take a mass of comparable cases to establish a rule.  As far as the logical structure goes, however, this quantitative confirmation only amounts to "gilding the lily".  Perfectly valid rules can be guessed on the first try, abstracted from a single experience or adopted vicariously with no personal experience.  Numerical factors only modify the degree of confidence and the strength of habit that govern the application of previously learned rules.
    
=====4.3.3.2. Inquiry=====
 
=====4.3.3.2. Inquiry=====
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Returning to the &ldquo;Rainy Day&rdquo; story, we find our hero presented with a surprising Fact:
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>C \Rightarrow A,</math>
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| width="60%" | "in the Current situation the Air is cool".
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| width="20%" | (Fact)
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|}
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Responding to an intellectual reflex of puzzlement about the situation, his resource of common knowledge about the world is impelled to seize on an approximate Rule:
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>B \Rightarrow A,</math>
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| width="60%" | "just Before it rains, the Air is cool".
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| width="20%" | (Rule)
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|}
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This Rule can be recognized as having a potential relevance to the situation because it matches the surprising Fact, <math>C \Rightarrow A,</math> in its consequential feature <math>A.\!</math>  All of this suggests that the present Case may be one in which it is just about to rain:
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>C \Rightarrow B,</math>
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| width="60%" | "the Current situation is just Before it rains".
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| width="20%" | (Case)
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|}
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The whole mental performance, however automatic and semi conscious it may be, that leads up from a problematic Fact and a knowledge base of Rules to the plausible suggestion of a Case description, is what we are calling abductive inference.
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The next phase of inquiry uses deductive inference to expand the implied consequences of the abductive hypothesis, with the aim of testing its truth.  For this purpose, the inquirer needs to think of other things that would follow from the consequence of his precipitate explanation.  Thus, he now reflects on the Case just assumed:
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>C \Rightarrow B,</math>
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| width="60%" | "the Current situation is just Before it rains".
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| width="20%" | (Case)
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|}
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He looks up to scan the sky, perhaps in a random search for further information, but since the sky is a logical place to look for details of an imminent rainstorm, symbolized in our story by the letter <math>B,\!</math> we may safely suppose that our reasoner has already detached the consequence of the abductive Case, <math>C \Rightarrow B,</math> and has begun to expand on its further implications.  So let us imagine that the up looker has a more deliberate purpose in mind, and that his search for new data is driven by the new found, determinate Rule:
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>B \Rightarrow D,</math>
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| width="60%" | "just Before it rains, Dark clouds appear".
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| width="20%" | (Rule)
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|}
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Contemplating the assumed Case in combination with this new Rule would lead him by an immediate deduction to predict an additional Fact:
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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| width="20%" | <math>C \Rightarrow D,</math>
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| width="60%" | "in the Current situation Dark clouds appear".
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| width="20%" | (Fact)
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|}
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The reconstructed picture of reasoning assembled in this second phase of inquiry is true to the pattern of deductive inference.
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Whatever the case, our subject observes a Dark cloud, just as he would expect on the basis of the new hypothesis.  The explanation of imminent rain removes the discrepancy between observations and expectations and thereby reduces the shock of surprise that made this inquiry necessary.
    
====4.3.4. Details of Induction====
 
====4.3.4. Details of Induction====
 +
 +
To understand the relevance of inductive reasoning to the closing phases of inquiry there are a couple of observations we should make.  First, we need to recognize that smaller inquiries are woven into larger inquiries, whether we view the whole pattern of inquiry as carried on by single agents or complex communities.  Next, we need to consider three distinct ways in which particular instances of inquiry can relate to an ongoing inquiry at a larger scale.  These inductive modes of interaction between inquiries may be referred to as the learning, transfer, and testing of rules.
 +
 +
Throughout inquiry the reasoner makes use of rules that have to be transported across intervals of experience, from masses of experience where they are learned to moments of experience where they are used.  Inductive reasoning is involved in the learning and transfer of these rules, both in accumulating a knowledge base and in carrying it through the times between acquisition and application.
 +
 +
Thus, the first way that induction contributes to an ongoing inquiry is through the learning of rules, that is, by creating each of the rules in the knowledge base that gets used along the way.  The second way is through the use of analogy, a two step combination of induction and deduction, to transfer rules from one context to another.  Finally, every inquiry making use of a knowledge base constitutes a &ldquo;field test&rdquo; of its accumulated contents.  If the knowledge base fails to serve any live inquiry in a satisfactory manner, then there may be reason to reconsider some of its rules.
 +
 +
I will now detail how these principles of learning, transfer, and testing apply to the ''Rainy Day'' example.
    
=====4.3.4.1. Learning=====
 
=====4.3.4.1. Learning=====
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 +
Rules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference.  For example, consider a proposition like the following:
 +
 +
{| align="center" cellpadding="0" cellspacing="0" width="90%"
 +
| width="20%" | <math>B \Rightarrow A,</math>
 +
| width="60%" | "just Before it rains, the Air is cool".
 +
| width="20%" | &nbsp;
 +
|}
 +
 +
Such a proposition is usually induced from a consideration of many past events, as follows.
 +
 +
{| align="center" cellpadding="0" cellspacing="0" width="90%"
 +
| width="20%" | <math>C \Rightarrow B,</math>
 +
| width="60%" | "in Certain events, it is just Before it rains".
 +
| width="20%" | (Case)
 +
|-
 +
| <math>C \Rightarrow A,</math>
 +
| "in Certain events, the Air is cool".
 +
| (Fact)
 +
|-
 +
| <math>B \Rightarrow A,</math>
 +
| "just Before it rains, the Air is cool".
 +
| (Rule)
 +
|}
 +
 +
However, the same proposition could also be abduced as an explanation of a singular occurrence or deduced as a conclusion of a prior theory.
    
=====4.3.4.2. Transfer=====
 
=====4.3.4.2. Transfer=====
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 +
What really gives a distinctively inductive character to the acquisition of a knowledge base is the "analogy of experience" that underlies its useful application.  Whenever we find ourselves prefacing an argument with the phrase, &ldquo;If past experience is any guide&nbsp;&hellip;&nbsp;&rdquo; we can be sure this principle has come into play.  We are invoking an analogy between past experience, considered as a totality, and present experience, considered as a point of application.  What we mean in practice is this:  &ldquo;If past experience is a fair sample of possible experience, then the knowledge gained in it applies to present experience.&rdquo;  This is the mechanism that allows a knowledge base to be carried across gulfs of experience that are indifferent to the effective contents of its rules.
 +
 +
Here are the details of how this works out in the ''Rainy Day'' example.  Let us consider a fragment <math>K\!</math> of the reasoner's knowledge base that is logically equivalent to the conjunction of two rules.
 +
 +
{| align="center" cellpadding="0" cellspacing="0" width="90%"
 +
| <math>K \Leftrightarrow (B \Rightarrow A) \land (B \Rightarrow D).</math>
 +
|}
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 +
It is convenient to have the option of expressing all logical statements in terms of their models, that is, in terms of the primitive circumstances or the elements of experience over which they hold true.  Let <math>C^-\!</math> be a chosen set of experiences, or the circumstances we have in mind when we refer to "past experience".  Let <math>C^+\!</math> be a collective set of experiences, or the projective total of possible circumstances.  Let <math>C\!</math> be a current experience, or the circumstances present to the reasoner.  If we think of the knowledge base <math>K\!</math> as referring to the "regime of experience" over which it is valid, then all of these sets of models can be compared by simple relations of set inclusion or logical implication.
 +
 +
In these terms, the "analogy of experience" proceeds by inducing a Rule about the validity of a current knowledge base and then deducing its applicability to a current experience.
 +
 +
{| align="center" cellpadding="0" cellspacing="0" width="90%"
 +
| width="20%" | <math>C^- \Rightarrow C^+,</math>
 +
| width="60%" | "Chosen events fairly sample Collective events".
 +
| width="20%" | (Case)
 +
|-
 +
| <math>C^- \Rightarrow K,</math>
 +
| "Chosen events support the Knowledge regime".
 +
| (Fact)
 +
|-
 +
| <math>C^+ \Rightarrow K,</math>
 +
| "Collective events support the Knowledge regime".
 +
| (Rule)
 +
|-
 +
| <math>C \Rightarrow C^+,</math>
 +
| "Current events fairly sample Collective events".
 +
| (Case)
 +
|-
 +
| <math>C \Rightarrow K,</math>
 +
| "Collective events support the Knowledge regime".
 +
| (Fact)
 +
|}
    
=====4.3.4.3. Testing=====
 
=====4.3.4.3. Testing=====
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 +
If the observer looks up and does not see dark clouds, or if he runs for shelter but it does not rain, then there is fresh occasion to question the validity of his knowledge base.
    
====4.3.5. The Stages of Inquiry====
 
====4.3.5. The Stages of Inquiry====
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 4|Part 4]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 4|Part 4]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5|Part 5]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5|Part 5]]
 +
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
 +
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
 +
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 8|Part 8]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
 
&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
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</div>
 
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[[Category:Artificial Intelligence]]
 
[[Category:Artificial Intelligence]]
Jon Awbrey
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