Sign Relational Complex
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Sign Relational Complex
In semiotics, a sign relational complex is a generalization of a sign relation that allows for empty components in the ''elementary sign relations'', or sign relational triples of the form (object, sign, interpretant). Generally speaking, when it comes to things that are being contemplated as ostensible or potential signs of other things, neither the existence nor the uniqueness of the elements appearing in the sign relation is guaranteed. For example, the reference of a putative sign to its putative objects may achieve reference to zero, to one, or to many objects. A proper treatment of this complication calls for the conception of something slightly more general than a sign relation proper, namely, a sign relational complex. In effect, expressed in the roughest practical terms, this allows for ''missing data'' in the columns of the relational database table for the sign relation in question. Typically one operates on the default assumption that all of the roles of elementary ...
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Semiotics
Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something, usually called a meaning, to the sign's interpreter. The meaning can be intentional such as a word uttered with a specific meaning, or unintentional, such as a symptom being a sign of a particular medical condition. Signs can also communicate feelings (which are usually not considered meanings) and may communicate internally (through thought itself) or through any of the senses: visual, auditory, tactile, olfactory, or gustatory (taste). Contemporary semiotics is a branch of science that studies meaning-making and various types of knowledge. The semiotic tradition explores the study of signs and symbols as a significant part of communications. Unlike linguistics, semiotics also studies non-linguistic sign systems. Semiotics includes th ...
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Sign Relation
A sign relation is the basic construct in the theory of signs, also known as semiotics, as developed by Charles Sanders Peirce. Anthesis Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive power, the sunflower would become a Representamen of the sun. (C.S. Peirce, "Syllabus" (''c''. 1902), ''Collected Papers'', CP 2.274). In his picturesque illustration of a sign relation, along with his tracing of a corresponding sign process, or ''semiosis'', Peirce uses the technical term ''representamen'' for his concept of a sign, but the shorter word is precise enough, so long as one recognizes that its meaning in a particular theory of signs is given by a specific definition of what it means to be a sign. Definition One of Peirce's clearest and most complete definitions of a sign is one that ...
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Ad Hoc
Ad hoc is a Latin phrase meaning literally 'to this'. In English, it typically signifies a solution for a specific purpose, problem, or task rather than a generalized solution adaptable to collateral instances. (Compare with ''a priori''.) Common examples are ad hoc committees and commissions created at the national or international level for a specific task. In other fields, the term could refer to, for example, a military unit created under special circumstances (see '' task force''), a handcrafted network protocol (e.g., ad hoc network), a temporary banding together of geographically-linked franchise locations (of a given national brand) to issue advertising coupons, or a purpose-specific equation. Ad hoc can also be an adjective describing the temporary, provisional, or improvised methods to deal with a particular problem, the tendency of which has given rise to the noun ''adhocism''. Styling Style guides disagree on whether Latin phrases like ad hoc should be italicized. ...
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Relation (mathematics)
In mathematics, a relation on a set may, or may not, hold between two given set members. For example, ''"is less than"'' is a relation on the set of natural numbers; it holds e.g. between 1 and 3 (denoted as 1 is an asymmetric relation, but ≥ is not. Again, the previous 3 alternatives are far from being exhaustive; as an example over the natural numbers, the relation defined by is neither symmetric nor antisymmetric, let alone asymmetric. ; : for all , if and then . A transitive relation is irreflexive if and only if it is asymmetric. For example, "is ancestor of" is a transitive relation, while "is parent of" is not. ; : for all , if then or . This property is sometimes called "total", which is distinct from the definitions of "total" given in the section . ; : for all , or . This property is sometimes called "total", which is distinct from the definitions of "total" given in the section . ; : every nonempty subset of contains a minimal element with respect to ...
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Semiotics
Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something, usually called a meaning, to the sign's interpreter. The meaning can be intentional such as a word uttered with a specific meaning, or unintentional, such as a symptom being a sign of a particular medical condition. Signs can also communicate feelings (which are usually not considered meanings) and may communicate internally (through thought itself) or through any of the senses: visual, auditory, tactile, olfactory, or gustatory (taste). Contemporary semiotics is a branch of science that studies meaning-making and various types of knowledge. The semiotic tradition explores the study of signs and symbols as a significant part of communications. Unlike linguistics, semiotics also studies non-linguistic sign systems. Semiotics includes th ...
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Semiosis
Semiosis (, ), or sign process, is any form of activity, conduct, or process that involves signs, including the production of meaning. A sign is anything that communicates a meaning, that is not the sign itself, to the interpreter of the sign. The meaning can be intentional such as a word uttered with a specific meaning, or unintentional, such as a symptom being a sign of a particular medical condition. Signs can communicate through any of the senses, visual, auditory, tactile, olfactory, or taste. The term was introduced by Charles Sanders Peirce (1839–1914) to describe a process that interprets signs as referring to their objects, as described in his theory of sign relations, or semiotics. Other theories of sign processes are sometimes carried out under the heading of semiology, following on the work of Ferdinand de Saussure (1857–1913). Overview Peirce was interested primarily in logic, while Saussure was interested primarily in linguistics, which examines the functio ...
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Sign Relation
A sign relation is the basic construct in the theory of signs, also known as semiotics, as developed by Charles Sanders Peirce. Anthesis Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive power, the sunflower would become a Representamen of the sun. (C.S. Peirce, "Syllabus" (''c''. 1902), ''Collected Papers'', CP 2.274). In his picturesque illustration of a sign relation, along with his tracing of a corresponding sign process, or ''semiosis'', Peirce uses the technical term ''representamen'' for his concept of a sign, but the shorter word is precise enough, so long as one recognizes that its meaning in a particular theory of signs is given by a specific definition of what it means to be a sign. Definition One of Peirce's clearest and most complete definitions of a sign is one that ...
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Sign System
A sign system is a key concept in semiotics and is used to refer to any system of signs and relations between signs. The term ''language'' is frequently used as a synonym for a sign-system. However, the term ''sign-system'' is considered preferable to the term ''language'' for a number of reasons. First, the use of the term ''language'' tends to carry with it connotations of human language, particularly human spoken language. Human spoken language is only one example of a sign-system, albeit probably one of the most complex sign-systems known. In traditional forms of face-to-face communication, humans communicate through non-verbal as well as verbal sign-systems; colloquially, this can be referred to as body language. Hence, humans communicate a great deal by way of facial movements and other forms of bodily expression. Such expressions are also signs and an organised collection of such signs would be considered a sign system. Tone of voice in spoken communication, conveys meani ...
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Simplicial Complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. To distinguish a simplicial from an abstract simplicial complex, the former is often called a geometric simplicial complex.'', Section 4.3'' Definitions A simplicial complex \mathcal is a set of simplices that satisfies the following conditions: :1. Every face of a simplex from \mathcal is also in \mathcal. :2. The non-empty intersection of any two simplices \sigma_1, \sigma_2 \in \mathcal is a face of both \sigma_1 and \sigma_2. See also the definition of an abstract simplicial complex, which loosely speaking is a simplicial complex without an associated geometry. A simplicial ''k''-complex \ ...
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Theory Of Relations
In mathematics, a finitary relation over sets is a subset of the Cartesian product ; that is, it is a set of ''n''-tuples consisting of elements ''x''''i'' in ''X''''i''. Typically, the relation describes a possible connection between the elements of an ''n''-tuple. For example, the relation "''x'' is divisible by ''y'' and ''z''" consists of the set of 3-tuples such that when substituted to ''x'', ''y'' and ''z'', respectively, make the sentence true. The non-negative integer ''n'' giving the number of "places" in the relation is called the '' arity'', ''adicity'' or ''degree'' of the relation. A relation with ''n'' "places" is variously called an ''n''-ary relation, an ''n''-adic relation or a relation of degree ''n''. Relations with a finite number of places are called ''finitary relations'' (or simply ''relations'' if the context is clear). It is also possible to generalize the concept to ''infinitary relations'' with infinite sequences. An ''n''-ary relation over sets i ...
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Triadic Relation
In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place. Just as a binary relation is formally defined as a set of ''pairs'', i.e. a subset of the Cartesian product of some sets ''A'' and ''B'', so a ternary relation is a set of triples, forming a subset of the Cartesian product of three sets ''A'', ''B'' and ''C''. An example of a ternary relation in elementary geometry can be given on triples of points, where a triple is in the relation if the three points are collinear. Another geometric example can be obtained by considering triples consisting of two points and a line, where a triple is in the ternary relation if the two points determine (are incident with) the line. Examples Binary functions A function in two variables, mapping two values from sets ''A'' and ''B'', respectively, to a value in ''C'' associate ...
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