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- ...e integer. In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math> ...ns. These play a basic role in questions of [[complexity theory]] as well as the design of circuits and chips for digital computers.5 KB (589 words) - 20:24, 5 November 2015
- ...say, <math>\mathbb{B} = \{ 0, 1 \},</math> whose elements are interpreted as [[logical value]]s, typically, <math>0 = \operatorname{false}</math> and <m ...h>x\!</math> is a [[variable]] that takes its value from a boolean domain, as <math>x \in \mathbb{B}.</math>5 KB (561 words) - 19:54, 5 November 2015
- ...<math>X\!</math> is an arbitrary set and where <math>\mathbb{B}</math> is a [[boolean domain]]. ...on. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding sign or syntactic expression.7 KB (806 words) - 21:14, 5 November 2015
- ...pecial type of [[relation (mathematics)|relational predicate]] that arises as the limit of an iterated process of [[hypostatic abstraction]]. ...cate to represent is the form of connection between the different subjects as expressed in the propositional ''form''. What I mean by “everyt8 KB (1,058 words) - 04:08, 10 November 2015
- ...ion''. The object of discussion or thought thus introduced is termed a ''[[hypostatic object]]''. ...ntroduced [[Charles Sanders Peirce]] (CP 4.235, “[[The Simplest Mathematics]]” (1902), in ''Collected Papers'', CP 4.227–323).7 KB (915 words) - 18:58, 10 November 2015
- A '''multigrade operator''' <math>\Omega\!</math> is a ''[[parametric operator]]'' with ''parameter'' <math>k\!</math> in the set ...math> is typically denoted with the parameter <math>k\!</math> left tacit, as the appropriate application is implicit in the number of operands listed.5 KB (618 words) - 04:12, 7 November 2015
- ...onal]] form which translates into being the [[graph (mathematics)|map]] of a ''realization'' [[digital network|network]] (see [[VHDL]]). ...ssor, which enables a user to perform a task, and [[system software]] such as an [[operating system]], which enables other software to run properly, by i14 KB (2,076 words) - 13:33, 31 October 2012
- ...tion, relation, and symbols in question it is first necessary to establish a few ideas about the connections among them. ...oximations to the concept of logical implication are expressed in ordinary language by means of linguistic forms like the following:16 KB (2,147 words) - 20:18, 4 November 2015
- ...ating all of the other operators in the subject matter variously described as [[boolean function]]s, monadic predicate calculus, [[propositional calculus ...s ''false''. Hence, the value of <math>x \curlywedge x</math> is the same as that of <math>\overline {x}</math>; and the value of <math>\underline {x \9 KB (1,221 words) - 15:04, 5 November 2015
- ...positional calculus]], and sentential logic. The term serves to mark a level of abstraction in which the more inessential differences among these ...abstract type <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}</math> in a number of different languages for zeroth order logic.10 KB (1,357 words) - 16:04, 8 November 2015
- ...reatment of relations by way of their corresponding relative terms affords a distinctive perspective on the subject, even though all angles of approach ...ning with his 1870 paper “[[Logic of Relatives (1870)|Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the7 KB (919 words) - 22:48, 10 November 2015
- <font size="3">☞</font> This page serves as a '''focal node''' for a collection of related resources. * [[Relation (mathematics)|Relation]]3 KB (396 words) - 19:32, 17 September 2020
- [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language] [http://intersci.ss.uci.edu/wiki/index.php/Propositions_As_Types Propositions As Types]15 KB (1,907 words) - 14:08, 9 October 2017
- ...known is a massive fan of football as all who know him will testify and is a season ticket holder at Anfield where he follows his beloved 'Redmen', Live Early life was hard for a young Craig Walton as he lived on a farm in Jersey where he grew up amongst various animals including his boyho5 KB (836 words) - 20:07, 3 July 2021
- [https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview Cactus Language] [https://oeis.org/wiki/Propositions_As_Types_Analogy Propositions As Types Analogy]16 KB (2,092 words) - 14:20, 14 January 2021
- ...''propositional logic'' (or ''sentential logic''). Propositional logic is a domain of formal subject matter that is, up to somorphism, constituted by t ...ubset of these expressions, plus a set of transformation rules that define a binary relation on the space of expressions.17 KB (2,301 words) - 15:56, 7 November 2015
- ...</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{A}</math> is the domain of logical values <math>\{ \operatorname{false}, \ope ...also possible, depending on the overall representation of truth functions as boolean functions. The remainder of this article assumes the usual represe16 KB (2,190 words) - 03:25, 30 October 2015
- '''Peirce's law''' is a formula in [[propositional calculus]] that is commonly expressed in the fol ...calculus determines whether Peirce's law is taken as an axiom or proven as a theorem.11 KB (1,526 words) - 04:14, 18 November 2015
- In mathematics, a '''finitary relation''' is defined by one of the formal definitions given b ...ation of ''order'' denoted by the sign “<math>{<}\!</math>” in a statement like <math>5 < 12.\!</math> Relations that involve two ''pl20 KB (2,925 words) - 17:08, 14 November 2015
- ...wo logical values, typically the values of two propositions, that produces a value of ''true'' just in case exactly one of its operands is true. * [[Relation (mathematics)|Relation]]6 KB (728 words) - 01:45, 31 October 2015
- ...uciens'' or the ''relational base'', each of which is properly simpler in a specified way than the relation under examination. ...''relation reconstruction''' or '''relational reconstructibility''', since a useful way of stating the question is to ask whether the reductandum can be29 KB (4,035 words) - 03:32, 15 November 2015
- A '''minimal negation operator''' <math>(\nu)~\!</math> is a logical connective that says “just one false” of its logical ar If the list of arguments is empty, as expressed in the form <math>\nu(),~\!</math> then it cannot be true that ex23 KB (3,337 words) - 13:54, 3 September 2017
- ...spective of combinatorics, in other words, as a subject matter in discrete mathematics, with special attention to finite structures and concrete set-theoretic con ...sed at a given time, it tends to become less clear as contexts collide, or as discussion moves from one context to another.25 KB (3,665 words) - 21:04, 16 November 2015
- ====A Modulating Prelude==== ====A Fugitive Canon====15 KB (1,597 words) - 12:00, 15 April 2017
- ...gs, including letters, manuscripts, publications, and Nachlass, along with a selection of secondary literature. * CE n, m = ''Writings of Charles S. Peirce: A Chronological Edition'', vol. n, page m.18 KB (2,307 words) - 21:04, 27 May 2015
- '''Relation composition''', or the composition of [[relation (mathematics)|relations]], is the generalization of function composition, or the composi ...the logic of 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) - 18:14, 14 November 2015
- ...ruct in the theory of signs, also known as [[semeiotic]] or [[semiotics]], as developed by Charles Sanders Peirce. ...d of doing so with the same reproductive power, the sunflower would become a Representamen of the sun. (C.S. Peirce, “Syllabus” (''c''.&nbs58 KB (8,260 words) - 03:40, 21 November 2016
- A '''logical graph''' is a graph-theoretic structure in one of the systems of graphical syntax that Ch ...ped several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.41 KB (5,845 words) - 14:26, 6 November 2015
- A '''logical graph''' is a [[graph theory|graph-theoretic]] structure in one of the systems of graphic ...ped several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.42 KB (5,905 words) - 21:49, 22 May 2010
- ...universe of discourse]] or transformations that map a source universe into a target universe. ...d <math>c\!</math> currently reside in region <math>Q\!</math> while <math>a\!</math> and <math>d\!</math> do not.158 KB (22,468 words) - 03:24, 27 December 2016
- ...ct, and its results. Although the questions are diverse and never-ending, a number of recurrent themes can be recognized: # What does it mean to refer to a mathematical object?73 KB (10,917 words) - 19:48, 6 September 2017
- ...tions and developed by means of definite rules of inference. The scope of a truth theory can be restricted to tightly-controlled and well-bounded unive ...concepts — meaning, reality, and values in general, to mention just a few.37 KB (5,460 words) - 14:45, 17 November 2015
- ...as ''belief'', ''certainty'', ''knowledge'', or ''truth'' is the result of a ''process'', namely, ''[[inquiry]]''. ...e often confused with a number of quite distinct notions, it is useful say a few words about these other theories, and to highlight the points of signif33 KB (4,907 words) - 04:32, 22 September 2014
- ...://status.wikimedia.org/ | Channel guidelines: http://bit.ly/WP-IRC | Need a chanop? Ask here or in #wikimedia-ops | For urgent admin help, say !admin < [17:28:48] <W3ird_N3rd> Elreycontrono, {soap|bed}, I improved it a little30 KB (3,790 words) - 00:52, 22 July 2015
- ...-to-be-tapped potential for many current issues, though it would take just a little bit of drilling to exploit its resources to the fullest that we can. ...er, with no real connection to physics intended, at least, not so directly as the picture at first suggests:73 KB (8,310 words) - 00:36, 27 April 2017
- ...al system with the expressive capacity to describe change and diversity in a logical universe of discourse. ...a universe of discourse or transformations that map a source universe into a target universe. This augments ordinary propositional calculus in the same131 KB (20,198 words) - 15:38, 2 December 2015
- ...rackets the way it would in the external wiki environment, in other words, as signature tags. [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk One of the first things that you can do, once you have a moderately efficient calculus for boolean functions or propositional logic,127 KB (18,875 words) - 13:28, 10 December 2014
- ...iples that govern the use of a ''differential logical calculus'', that is, a formal system with the expressive capacity to describe change and diversity ...a universe of discourse or transformations that map a source universe into a target universe. This augments ordinary propositional calculus in the same145 KB (19,916 words) - 19:32, 11 December 2014
- have a really decent calculus for boolean functions Start with a proposition of the form x & y, which134 KB (14,931 words) - 13:30, 5 December 2014
- ...rial was removed from the Wikipedia article by inept editors and placed in a [http://en.wikipedia.org/wiki/Talk:Charles_Sanders_Peirce/Cache cache subpa ...als]], and not a position in the [[realist]] vs. [[idealist]] debate about a mind-independent [[reality]]. Peirce's scholastic realism in fact supplies74 KB (11,616 words) - 23:56, 21 May 2010
- ...ork follows on the ''alpha graphs'' that Charles Sanders Peirce devised as a graphical syntax for [[propositional calculus]] and also on the ''calculus ...quo; via Spencer-Brown's ''Laws of Form'' (LOF). In formal proofs, we use a variation of the annotation scheme from LOF to mark each step of the proof157 KB (17,761 words) - 03:44, 10 November 2016
- ...he paper bridges that Peirce used to augment his genus, can be represented as parse-strings in Ascii and sculpted into pointer-structures in computer mem ...confusing unless the logical expression under consideration is set off in a separate display.168 KB (21,027 words) - 12:41, 6 August 2017
- ...graphs are called ''cacti'' by graph theorists. Hence the name ''[[cactus language]]'' for this dialect of propositional calculus. ...and the same proposition might be reached from three different directions, as the end result of an inference in each of the three modes.106 KB (13,991 words) - 18:45, 18 March 2020
- Recent postings on blogs and discussion lists have brought to mind a congeries of perennial themes out of Peirce. I am prompted to collect what ''For the Time Being, a Sleightly Random Recap of Notes …''105 KB (16,763 words) - 20:36, 26 August 2017
- ...mployed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or ''[[semeiotic]]'', that he is larg ...er the philosophies of knowledge, language, and science. Peirce saw logic as the formal branch of the theory of signs, or ''[[semiotics]]'', here using93 KB (14,277 words) - 20:00, 28 July 2017
- {{DISPLAYTITLE:Cactus Language}} ...be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions,211 KB (31,551 words) - 20:44, 2 August 2017
- The following language is useful in describing the facts represented by the venn diagram. * The universe of discourse is a set, <math>X,\!</math> represented by the area inside the large rectangle.369 KB (46,156 words) - 04:20, 27 December 2016
- ...ture of inquiry processes, with an eye to those elements that can be given a computational basis. ...all intelligent software systems in the future. In any application where a knowledge base is maintained, it will become more and more important to exa121 KB (16,341 words) - 04:34, 30 October 2015
- the microscope and look at a few of its finer details. In particular, I can use it to illustrate a couple of139 KB (16,717 words) - 14:30, 12 September 2017
- \mathrm{a}. & \text{animal} \mathit{a}. & \text{enemy}226 KB (33,992 words) - 16:22, 29 December 2017
