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  • ...of two propositions, that produces a value of ''true'' if and only if both of its operands are true. The [[truth table]] of <math>p ~\operatorname{AND}~ q,</math> also written <math>p \land q\!</math
    5 KB (658 words) - 02:02, 31 October 2015
  • A '''logical graph''' is a graph-theoretic structure in one of the systems of graphical syntax that Charles Sanders Peirce developed for logic. ...ve graphs'', and ''existential graphs'', Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be
    41 KB (5,845 words) - 14:38, 6 November 2015
  • ==History== Here is Peirce's own statement and proof of the law:
    11 KB (1,526 words) - 16:14, 18 November 2015
  • ...inguished from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other. Two definitions of the relation concept are common in the literature. Although it is usually
    25 KB (3,665 words) - 21:05, 16 November 2015
  • ...ion (mathematics)|polyadic or finitary relation]], one in which the number of places in the relation is three. In other language that is often used, a t ...Therefore it will be useful to consider a few concrete examples from each of these two realms.
    20 KB (2,655 words) - 21:25, 16 November 2015
  • A '''sign relation''' is the basic construct in the theory of signs, also known as [[semeiotic]] or [[semiotics]], as developed by Charle ...th the same reproductive power, the sunflower would become a Representamen of the sun. (C.S. Peirce, &ldquo;Syllabus&rdquo; (''c''.&nbsp;1902), ''Collec
    58 KB (8,251 words) - 21:35, 15 November 2015
  • ...})\!</math> is a logical connective that says &ldquo;just one false&rdquo; of its logical arguments. ...orm <math>\texttt{Mno}(),\!</math> then it cannot be true that exactly one of the arguments is false, so <math>\texttt{Mno}() = \texttt{False}.\!</math>
    22 KB (3,319 words) - 19:22, 6 November 2015
  • ...ath> in the '''parameter set''' <math>\Alpha\!</math> is an indexed family of operators <math>(\Omega_\alpha)_\Alpha = \{ \Omega_\alpha : \alpha \in \Alp * [[Universe of discourse]]
    5 KB (572 words) - 04:18, 7 November 2015
  • ...ter that is, up to somorphism, constituted by the structural relationships of mathematical objects called ''propositions''. ...s a set of transformation rules that define a binary relation on the space of expressions.
    17 KB (2,301 words) - 16:02, 7 November 2015
  • ...ators is a ''[[sole sufficient operator]]'' for deriving or generating all of the other operators in the subject matter variously described as [[boolean ...<math>\mathbf{f}</math>, because it is necessarily false; while the value of <math>\underline {x \curlywedge y} \curlywedge \underline {x \curlywedge y}
    9 KB (1,221 words) - 15:05, 5 November 2015
  • * [[Universe of discourse]] * [[Logic of relatives]]
    5 KB (561 words) - 19:56, 5 November 2015
  • ...case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math> ...y a basic role in questions of [[complexity theory]] as well as the design of circuits and chips for digital computers.
    5 KB (589 words) - 20:25, 5 November 2015
  • A '''boolean-valued function''' is a function of the type <math>f : X \to \mathbb{B},</math> where <math>X\!</math> is an ar ...cteristic function, indicator function, predicate, or proposition. In all of these uses it is understood that the various terms refer to a mathematical
    7 KB (806 words) - 21:16, 5 November 2015
  • ...expressive capacity to describe change and diversity in logical universes of discourse. ...differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.
    6 KB (662 words) - 22:34, 5 November 2015
  • ...ks, for example, &ldquo;lover&nbsp;of&nbsp;__&rdquo;, or &ldquo;giver&nbsp;of&nbsp;__&nbsp;to&nbsp;__&rdquo;. * [[Universe of discourse]]
    5 KB (599 words) - 20:22, 16 November 2015
  • ...cs)|relational predicate]] that arises as the limit of an iterated process of [[hypostatic abstraction]]. Here is one of Peirce's definitive discussions of the concept:
    8 KB (1,058 words) - 04:10, 10 November 2015
  • ...cation'', ''reification'', and ''subjectal abstraction''.&nbsp; The object of discussion or thought thus introduced is termed a ''[[hypostatic object]]'' ...ntroduced [[Charles Sanders Peirce]] (CP&nbsp;4.235, &ldquo;[[The Simplest Mathematics]]&rdquo; (1902), in ''Collected Papers'', CP&nbsp;4.227&ndash;323).
    7 KB (915 words) - 18:58, 10 November 2015
  • ...s affords a distinctive perspective on the subject, even though all angles of approach must ultimately converge on the same formal subject matter. ...es, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic]]&rdquo;.
    7 KB (919 words) - 22:54, 10 November 2015
  • ...rix affords a matrix representation of a <math>k\!</math>-adic [[relation (mathematics)|relation]]. * [[Universe of discourse]]
    5 KB (541 words) - 16:16, 11 November 2015
  • In mathematics, a '''finitary relation''' is defined by one of the formal definitions given below. ...math>&rdquo; in a statement like <math>5 + 7 = 12\!</math> or the relation of ''order'' denoted by the sign &ldquo;<math>{<}\!</math>&rdquo; in a stateme
    20 KB (2,925 words) - 17:10, 14 November 2015
  • ...omposition, or the composition of functions.&nbsp; The following treatment of relation composition takes the &ldquo;strongly typed&rdquo; approach to rel ...relative terms, in set theories of various kinds, and through a broadening of category theory from functions to relations in general.
    65 KB (6,802 words) - 18:18, 14 November 2015
  • ...', the ''factor'', or the ''method of construction'', plus a specified set of other relations, called the ''faciens'', the ''ingredients'', or the ''maki [[Relation composition]] and [[relation reduction]] are special cases of relation constructions.
    5 KB (621 words) - 19:24, 14 November 2015
  • ...ther relations, called the ''reduciens'' or the ''relational base'', each of which is properly simpler in a specified way than the relation under examin ...construction''' or '''relational reconstructibility''', since a useful way of stating the question is to ask whether the reductandum can be reconstructed
    29 KB (4,035 words) - 03:36, 15 November 2015
  • ...s <math>\{ \operatorname{false}, \operatorname{true} \}.</math> The names of the logical values, or ''truth values'', are commonly abbreviated in accord ...all representation of truth functions as boolean functions. The remainder of this article assumes the usual representation, taking the equations <math>\
    16 KB (2,190 words) - 18:31, 7 November 2015
  • The term '''''universe of discourse''''' is generally attributed to Augustus De&nbsp;Morgan (1846).&n ...of our discourse are found, that field may properly be termed the universe of discourse. (Boole 1854/1958, p.&nbsp;42).</p>
    6 KB (702 words) - 19:14, 7 November 2015
  • ...ate every operator in a specified class of operators.&nbsp; In the context of [[logic]], it is a logical operator that suffices to generate every [[boole * [[Universe of discourse]]
    5 KB (626 words) - 18:10, 7 November 2015
  • ...al calculus]], and sentential logic.&nbsp; The term serves to mark a level of abstraction in which the more inessential differences among these subjects ...ype <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}\!</math> in a number of different languages for zeroth order logic.
    12 KB (1,631 words) - 03:08, 9 November 2015
  • ...of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim. ...' must necessarily be predicated of all ''C''. &hellip; I call this kind of figure the First. (Aristotle, ''Prior Analytics'', 1.4).</p>
    58 KB (7,676 words) - 22:36, 15 November 2015
  • ...f logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. (Peirce, "On Time and Thought", CE&nbsp;3, 68 ...approach, it is possible to see a question of articulation and a question of explanation:
    24 KB (3,783 words) - 00:28, 16 November 2015
  • ...adic]] [[sign relations]], along with ''semiotic'' and the plural variants of both terms. The form ''semeiotic'' is often used to distinguish Peirce's t ==Types of signs==
    9 KB (1,162 words) - 21:30, 3 November 2015
  • ...notation and connotation, or, in roughly equivalent terms, by the concepts of extension and comprehension. ...rvard University (1865) and the Lowell Institute (1866).&nbsp; Here is one of the starting points:
    8 KB (1,038 words) - 03:26, 16 November 2015
  • ...se, advising the addressee on an optimal way of &ldquo;attaining clearness of apprehension&rdquo;. ==Seven ways of looking at a pragmatic maxim==
    12 KB (1,764 words) - 04:35, 17 November 2015
  • ...ell-bounded universes of discourse or its horizon may extend to the limits of the human imagination. Notions of truth are notoriously difficult to disentangle from many of our most basic concepts &mdash; meaning, reality, and values in general, to
    37 KB (5,460 words) - 14:50, 17 November 2015
  • ...ccumulated body of provisional knowledge, that seeks to discover good ways of achieving recognized aims, ends, goals, objectives, or purposes. * [[Universe of discourse]]
    5 KB (547 words) - 22:44, 16 November 2015
  • ...l knowledge, that seeks to discover what is true about a recognized domain of phenomena. * [[Universe of discourse]]
    5 KB (535 words) - 21:56, 16 November 2015
  • ...ogical [[function (mathematics)|function]], a specific logical [[relation (mathematics)|relation]], and the various symbols that are used to denote this function ...concept of logical implication are expressed in ordinary language by means of linguistic forms like the following:
    16 KB (2,147 words) - 20:20, 4 November 2015
  • ...o propositions, that produces a value of ''true'' just in case exactly one of its operands is true. The [[truth table]] of <math>p ~\operatorname{XOR}~ q,</math> also written <math>p + q\!</math> or
    6 KB (728 words) - 01:46, 31 October 2015
  • ...' with ''parameter'' <math>k\!</math> in the set <math>\mathbb{N}\!</math> of non-negative integers. ...math> left tacit, as the appropriate application is implicit in the number of operands listed. Thus <math>\Omega (x_1, \ldots, x_k)\!</math> may be take
    5 KB (618 words) - 04:12, 7 November 2015
  • ...al values, typically the values of two propositions, that produces a value of ''true'' if and only if both operands are false or both operands are true. The [[truth table]] of <math>p ~\operatorname{EQ}~ q,</math> also written <math>p = q,\!</math> <m
    5 KB (664 words) - 04:24, 4 November 2015
  • ...f two propositions, that produces a value of ''false'' if and only if both of its operands are false. The [[truth table]] of <math>p ~\operatorname{OR}~ q,</math> also written <math>p \lor q,\!</math>
    5 KB (656 words) - 00:56, 2 November 2015
  • ...n other words, it produces a value of ''true'' if and only if at least one of its operands is false. The [[truth table]] of <math>p ~\operatorname{NAND}~ q,</math> also written <math>p \stackrel{\cir
    5 KB (684 words) - 23:00, 4 November 2015
  • ...other words, it produces a value of ''false'' if and only if at least one of its operands is true. The [[truth table]] of <math>p ~\operatorname{NNOR}~ q,</math> also written <math>p \curlywedge q,
    5 KB (678 words) - 03:54, 5 November 2015
  • ...n, that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true. The [[truth table]] of <math>\operatorname{NOT}~ p,</math> also written <math>\lnot p,\!</math> ap
    6 KB (729 words) - 14:18, 5 November 2015