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, 16:16, 25 May 2007→1.3.4.2. Sign Relations : A Primer: markup
One aspect of semantics is concerned with the reference that a sign has to its object, which is called its ''denotation''. For signs in general, neither the existence nor the uniqueness of a denotation is guaranteed. Thus, the denotation of a sign can refer to a plural, a singular, or a vacuous number of objects. In the pragmatic theory of signs, these references are formalized as certain types of dyadic relations that are obtained by projection from the triadic sign relations.
One aspect of semantics is concerned with the reference that a sign has to its object, which is called its ''denotation''. For signs in general, neither the existence nor the uniqueness of a denotation is guaranteed. Thus, the denotation of a sign can refer to a plural, a singular, or a vacuous number of objects. In the pragmatic theory of signs, these references are formalized as certain types of dyadic relations that are obtained by projection from the triadic sign relations.
The dyadic relation that constitutes the ''denotative component'' of a sign relation L is denoted by "Den(L)". Information about the denotative component of semantics can be derived from L by taking its ''dyadic projection'' on the plane that is generated by the object domain and the sign domain, indicated by any one of the equivalent forms, "ProjOS(L)", "LOS", or "L12", and defined as follows:
The dyadic relation that constitutes the ''denotative component'' of a sign relation '''L''' is known as ''Den''('''L'''). Information about the denotative component of semantics can be derived from '''L''' by taking its ''dyadic projection'' on the plane that is generated by the object domain and the sign domain, indicated by any one of the equivalent forms, ''Proj''<sub>''OS''</sub>'''L''', '''L''<sub>''OS''</sub>, or '''L'''<sub>12</sub>, and defined as follows:
Den(L) = ProjOS(L) = LOS = {‹o, s› ? O?S : ‹o, s, i› ? L for some i ? I}.
* ''Den''('''L''') = ''Proj''<sub>''OS''</sub>'''L''' = '''L'''<sub>''OS''</sub> = {‹o, s› ∈ ''O'' × ''S'' : ‹o, s, i› ∈ '''L''' for some ''i'' ∈ ''I''}.
Looking to the denotative aspects of the present example, various rows of the Tables specify that A uses "i" to denote A and "u" to denote B, whereas B uses "i" to denote B and "u" to denote A. It is utterly amazing that even these impoverished remnants of natural language use have properties that quickly bring the usual prospects of formal semantics to a screeching halt.
Looking to the denotative aspects of the present example, various rows of the Tables specify that ''A'' uses "i" to denote ''A'' and "u" to denote ''B'', whereas ''B'' uses "i" to denote ''B'' and "u" to denote ''A''. It is utterly amazing that even these impoverished remnants of natural language use have properties that quickly bring the usual prospects of formal semantics to a screeching halt.
The other dyadic aspects of semantics that might be considered concern the reference that a sign has to its interpretant and the reference that an interpretant has to its object. As before, either type of reference can be multiple, unique, or empty in its collection of terminal points, and both can be formalized as different types of dyadic relations that are obtained as planar projections of the triadic sign relations.
The other dyadic aspects of semantics that might be considered concern the reference that a sign has to its interpretant and the reference that an interpretant has to its object. As before, either type of reference can be multiple, unique, or empty in its collection of terminal points, and both can be formalized as different types of dyadic relations that are obtained as planar projections of the triadic sign relations.