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...nal base'', each of which is properly simpler in a specified way than the relation under examination. ...eduction or relational reducibility is sometimes posed as a question of '''relation reconstruction''' or '''relational reconstructibility''', since a useful wa

...ns, many of which arise quite naturally in applications. This approach to relation theory, or the theory of relations, is distinguished from, though closely r Two definitions of the relation concept are common in the literature. Although it is usually clear in cont

...codifying a special type of uncertainty as to ''what regulative principle has any chance of success'', but the chief uncertainty is that we are called on ...ing present, serves to reduce the uncertainty of a decision that the agent has to make, whether it concerns the actions that the agent ought to take in or

...codifying a special type of uncertainty as to ''what regulative principle has any chance of success'', but the chief uncertainty is that we are called on ...ing present, serves to reduce the uncertainty of a decision that the agent has to make, whether it concerns the actions that the agent ought to take in or

...codifying a special type of uncertainty as to ''what regulative principle has any chance of success'', but the chief uncertainty is that we are called on ...ing present, serves to reduce the uncertainty of a decision that the agent has to make, whether it concerns the actions that the agent ought to take in or

...most commonly cited problem for the correspondence theory is defining the relation of correspondence, and ''when'' a proposition corresponds with the facts.&n ...there must ''exist'' some fact to which it corresponds: the proposition P has to correspond with the fact that P, if the proposition P is true. So, we ca

...these expressions, plus a set of transformation rules that define a binary relation on the space of expressions. ...rules are typically intended to preserve some type of semantic equivalence relation among the expressions. In particular, when the expressions are interpreted

...\mathrm{false}~\!</math> and <math>1 = \mathrm{true}.~\!</math>&nbsp; This has the following consequences: ...on of <math>x~\!</math> and <math>y,~\!</math> while its fiber of 1 is the relation of inequality between <math>x~\!</math> and <math>y.~\!</math>

...ave something to do with the dynamics of inquiry. This broad subject area has a part that is given by nature and a part that is ruled by nurture. On fi ...ils of thought that led him to develop a ''[[theory of signs]]'', one that has come to be known as '[[semiotic]]', and tracking next the ways of thinking

...ly typed&rdquo; approach to relations that is outlined in the article on [[relation theory]]. The first order of business is to define the operation on [[relation (mathematics)|relations]] that is variously known as the ''composition of r

...ropositional form <math>x \Rightarrow y\!</math> is equivalent to an order relation <math>x \le y\!</math> on the boolean values <math>0, 1 \in \mathbb{B},\!</ ...im &mdash; conveys more information &mdash; than the claim that the 2-adic relation <math>p \le r\!</math> holds between the two propositions <math>p\!</math>

A '''sign relation''' is the basic construct in the theory of signs, also known as [[semeiotic In his picturesque illustration of a sign relation, along with his tracing of a corresponding sign process, or ''[[semiosis]]'

meaning that every Boolean algebra, however small or large, has two constants or "nullary" operations, four unary operations, 16 binary ope meaning that every Boolean algebra, however small or large, has two constants or "nullary" operations, four unary operations, 16 binary ope

...f machine [[machine code|instructions]]. Some software, however, is of a [[relation (mathematics)|relational]] form which translates into being the [[graph (ma ...piling, interpreter, debugging, tracing, and etc., because the IDE usually has an advanced ''graphical user interface,'' or GUI.

...and ''model theory''. Another association of longstanding interest is the relation between truth and ''logical validity'', "because the fundamental notion of ...d strategy for approaching their complexity is to consider the [[two-place relation]]s that are left when the presence of a selected domain is simply ignored.

...left Q \upharpoonright (x) = \underline{1}</math> in any context where one has a relatively fixed <math>Q \subseteq X</math> in mind and where one is conc ...By the time one arrives in the "consequence box" of either Rule, then, one has in mind a comparatively fixed <math>Q \subseteq X,</math> a proposition <ma

...be taken as a boolean function <math>f(p, q)\!</math> having the abstract type <math>f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},</math> where <math>\ ...bb{B},</math> plus and minus are identical operations. This will make the relation between the differential and the integral parts of the appropriate calculus

...ount of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim. <p>Induction, or inductive reasoning, consists in establishing a relation between one extreme term and the middle term by means of the other extreme;

...be taken as a boolean function <math>f(p, q)\!</math> having the abstract type <math>f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},\!</math> where <math ...{B},\!</math> plus and minus are identical operations. This will make the relation between the differential and the integral parts of the appropriate calculus

a common data structure fundamental algorithms for one type of inductive learning and one type of deductive reasoning.

This report discusses C.S. Peirce's treatment of analogy, placing it in relation to his overall theory of inquiry. The first order of business is to introd ...bsp;&nbsp;&nbsp;&nbsp; If I reason that certain conduct is wise because it has a character which belongs ''only'' to wise things, I reason ''à&nbsp;prior

| has changed with time. usually come up in mathematics, namely, in relation to the problem

...be taken as a boolean function <math>f(x, y)\!</math> having the abstract type <math>f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},\!</math> where <math ...rential operators in a logical context, but the exploration of these ideas has been hampered by a number of factors, not the least of which being a syntax

...ss components of information about their own states. A system of this kind has its dynamics best understood only if we interpret some of its dimensions of ...e clearing up of definitions fall to the end, but that is how it sometimes has to be.

In the case of a propositional expression <math>Q\!</math> that has no token of the designated variable <math>x,\!</math> let it be stipulated The logical graph that concludes this proof is a variant type of ''disjunctive normal form'' (DNF) for the logical graph that was to be d

having the abstract type f : B x B -> B, where B = {0, 1} is context, but the exploration of these ideas has been hampered

...il the concrete species of dynamic data structures that we need. The time has come to flesh out the skeletons that we've drawn up to this point. ...s commonly describe it as a ''pointer'' and semioticians recognize it as a type of sign called an ''index''.

...il the concrete species of dynamic data structures that we need. The time has come to flesh out the skeletons that we've drawn up to this point. ...s commonly describe it as a ''pointer'' and semioticians recognize it as a type of sign called an ''index''.

Figure 1. Sign Relation in Dewey's "Rainy Day Inquiry" | the sign relation as follows: 'coolness' is a Sign of

==Relation to mathematics proper== ...hematics from the philosophy of mathematicians. Philosophy of mathematics has its source in any moment that a person reflects on mathematical practice, w

...e <math>q\!</math> is <math>\mathrm{false}\!</math> while <math>d\!</math> has moved from the region where <math>q\!</math> is <math>\mathrm{false}\!</mat ...nterpolates a new quality that is specifically tailored to account for the relation between Figure&nbsp;1 and Figure&nbsp;2.

...these senses, independence is a particular kind of relation, not a lack of relation, and certainly not a form of disconnection or exclusion. Second, Peirce di ...f Peirce’s writings (1984). More recently this way of understanding Peirce has been indepenently challenged by Rosa Mayorga in her ''On Universals'' (2002

...second class embraces terms whose logical form involves the conception of relation, and which require the addition of another term to complete the denotation. ...s terms whose logical form involves the conception of bringing things into relation, and which require the addition of more than one term to complete the denot

...fic ''address''.&nbsp; For semioticians, an address can be recognized as a type of index, and is commonly spoken of, on analogy with demonstrative pronouns ...e, any set is a COSI, so any relation in extension is a COSI, but a 1-adic relation is just a set of 1-tuples, that are in some lights indiscernible from their

...demic journal specializing in Peirce, pragmatism, and American philosophy, has appeared since 1965. Peirce has come to enjoy a significant international following. There are university r

...ble way around their real obstacles or through their apparent obstructions has to be found before proceeding. ...one refers to it by means of the word "duck" (this is a sign) and one has has an image of the duck in one's mind (this is an idea).

...lled by the type of sign that makes it up or whether it is named after the type of object that its signs are intended to denote, one may refer to this cact ...ype of character, and also to refer any blank we choose as a token of this type, referring to either of them in a marked way, but without the use of quotat

...hese questions the same way, but I will describe how I approach them, what has resulted so far, and what directions I plan to explore next. ...introduce the concept of an "inquiry driven system". In rough terms, this type of system is designed to integrate the functions of data-driven adaptive sy

...tension, and intention &mdash; but this is not the kind of definition that has to be taken on faith, or that constitutes the first and the last word on th ...ic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states tha

...ence", either that two things are recognisably different or that one thing has changed with time.</p> ...differentials of any functions usually come up in mathematics, namely, in relation to the problem of computing "locally linear approximations" to the more arb

...iably, war presents to those involved a certain risk of death; however, it has long been accepted, or at least considered, that civilian populations shoul ...The Eighth Air Force, for the time, had to give up any more raids of this type.

The '''Zuvela''' surname has strong roots originating from the western end of the island of Korcula in [ ...The book has many translations of old records of the Venetian Republic in relation to Korčula (from Venetian-Italian to standard Croatian).</ref>

...ibune published June 9, 1991. The use of life-safety bonds, it continued, "has evolved into an almost unlimited checking account for school districts . . ...to taxpayers in the 1980's in Cook County and the 5 collar counties alone has been $1 billion, Table 2.

The methodology that underlies this approach has two components: The analytic component involves describing the performance ...the phenomenon of interest, either in nature or on the computer, then one has reason to consider them further as possible explanations.

...supposed reciprocity between extensions and intensions, Peirce, of course, has another idea, and I would say a better idea, in part, because it forms the ...at might mean is a much longer story, the end of which your present teller has yet to reach. So, this time around, I will take up the story near the end

...istorical points, which never really count against a current practice that has gained a life of its own, this usage does have a further disadvantage of cu ...sup>''n''</sup>&nbsp;&rarr;&nbsp;'''B'''), and we may abbreviate this last type designation as '''B'''^''n''&nbsp;+&rarr;&nbsp;'''B''', or even m

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| in its arguments) and which has a continuous right inverse, all satisfying | one always has the equality:

...istorical points, which never really count against a current practice that has gained a life of its own, this usage does have a further disadvantage of cu ...}^n, (\mathbb{B}^n \to \mathbb{B}),</math> and we may abbreviate this last type designation as <math>\mathbb{B}^n\ +\!\to \mathbb{B},</math> or even more s

...istorical points, which never really count against a current practice that has gained a life of its own, this usage does have a further disadvantage of cu ...}^n, (\mathbb{B}^n \to \mathbb{B}),</math> and we may abbreviate this last type designation as <math>\mathbb{B}^n\ +\!\to \mathbb{B},</math> or even more s

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...was surprising at first to see these old issues rise again, but the shock has turned to recognition. A motion to reinstate thought with action, to amalg The concept of intelligence laid out here has been abstracted from two capacities that it both requires and supports: kn

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...ction of a ''reflective interpretive framework'' (RIF). This is a special type of sign-theoretic setting, illustrated in the present case by building on t ...an informal manner, located within a broader cultural context, and put in relation to the ways that intelligent agents can come to develop characteristic beli

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having the abstract type f : B x B -> B, where B = {0, 1} is context, but the exploration of these ideas has been hampered

| Every logical notation hitherto proposed has an unnecessary number of signs. | logical relation, that of illation, expressed by 'ergo'. A proposition,

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:''Note: For convenience, this very large multi-day log has been split into the following single-day logs: '''The log as originally formatted consists of 1,652,961 characters, so it has been hidden, for the benefit of users on mobile devices. It can be viewed [

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