Changes

: <math>\operatorname{Den}(L) = \operatorname{proj}_{OS} L = L_{OS} = \{ (o, s) \in O \times S : (o, s, i) \in L ~\text{for some}~ i \in I \}</math>.

: <math>\operatorname{Den}(L) = \operatorname{proj}_{OS} L = L_{OS} = \{ (o, s) \in O \times S : (o, s, i) \in L ~\text{for some}~ i \in I \}</math>.

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 <math>\text{A}</math> uses <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}</math> to denote <math>\text{A}</math> and <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}</math> to denote <math>\text{B}</math>, whereas <math>\text{B}</math> uses <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}</math> to denote <math>\text{B}</math> and <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}</math> to denote <math>\text{A}</math>.  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.