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a universe of discourse, has a unique and pre- K = K −{σ }. A member of the set K is
0

cise meaning. This definition, which is appro- denoted σ , j a positive integer indexing K .
j
priate for computation but not for linguistics, Then σ is considered to be an elementary sym-
0
eliminates multiple connotations for a single bol,or semiote, if three conditions are fulfilled.
term except as it can be recursively fragmented to
(i.) well-formed. There is one and only one
othertermshavinguniquesemantics.Inthatcase,
well-formed mapping ω such that ω: σ −→
0
however, the ultimate terms would necessarily be
ω(σ ).
0
used in preference to the more connotation-rich
(ii.) unique. The symbol σ and its seman-
term. The language can be formal or not, though 0
tics, ω(σ ), are unique, or
0
it is more likely that any arbitrary mapping will
be unique if it is derived from a formal language. σ = σ ,ω(σ ) = ω(σ ),
0
j
j
0
Of course, natural language is used to describe

the phenomenal universe and the objects within ∀ σ ∈ K , ω(σ ) ∈ ;(K ).
j
j
it (see representation); the meanings of terms in (iii.) elementary. Denote the set of all possi-
the natural language are mental constructs. Thus ble constructs of symbols in K by C , and a par-

in defining the natural language term “reaction” ticular construct, c , k a positive integer index.
k
corresponding to a biochemical transformation Then σ is elementary if, for a well-formed map-
0
(the object), one specifies the type of informa- ping ω, the semantics of every construct, ω(c ),
k
tion understood — chemical mechanism, kinetic is not equal to the semantics of σ , ω(σ ),or
0
0
regime, formal equation, etc., fragmenting the
term into a set of terms, then mapping each term ω(σ ) = ω(c ), ∀ c ∈ C .

0
k
k
to a meaning. The representation of the object
The semiote σ is denoted ς. Every semiote has
0
in the database is arbitrary and independent of
four properties:
the term referencing that object. Semantics are
distinct from database schemata, which describe (i.) its formally defined, computable seman-
the relationships among objects internal to the tics;
database but depend on the observer to recognize (ii.) its formally defined, computable syntax;
the mappings. This notion of semantics echoes
(iii.) its informally defined, natural language
that of conceptual graphs, but without depending
semantics; and
upon its graphical apparatus. See also represen-
(iv.) its informally defined, natural language
tation, semiote, and term semantics.
syntax.
semidefinite program Min {cx : S(x) ∈ The set of all semiotes is denoted K , and is
ς
P }, where P is the class of positive semidefi- also called the semantic basis set. A construct
nite matrices, and S(x) = S + Sum {x(j)S }, of semiotes is called a bundle of semiotes or a
0
j
j
where each S , for j = 0,...,n is a (given) sym- semiotic bundle.
j
metric matrix. This includes the linear program Comment: For the natural world there are
as a special case. as many mental models and domain models as
there are scientists and databases. Some of
semi-infiniteprogram Amathematicalpro- their terms’ semantics and representations will
gram with a finite number of variables or con- be isomorphic among people and databases (and
straints, but an infinite number of constraints between people and databases), but many will
or variables, respectively. The randomized pro- not. Semiotes, singly or more usually com-
gram is a semi-infinite program because it has an bined, are intended to map between the multiple
infinite number of variables when X is not finite. meanings humans assign to terms of a lan-
guage describing the phenomenal world and
semiote A semiote is a symbol denoting the the multiple ways in which objects and oper-
semantics of a useful elementary part of an idea, ations on them from that world can be repre-
datum, or computation. sented in databases. The proposition is that an
More formally, let a symbol be denoted σ and abstract layer of semiotes, incrementally and dis-
0
the set of all symbols other than σ be denoted tributively formulated and maintained, clearly
0
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC