ONT Re: Apposite Purposes Of Logical Languages Objectified (APOLLO)
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
My purpose here is to use the material of a few concrete
and fairly simple formal languages to illustrate how the
pragmatic theory of signs might be taken as a conceptual
staging ground for investigating an array of problems in
applied and computationally implemented logical systems.
Let now focus on the various formal languages that
we have been using for logical forms in ZOL(p, q),
or, more abstractly, at the level of ZOL(2).
Bin(2) = {"f_0000", "f_0001", "f_0010", "f_0011",
"f_0100", "f_0101", "f_0110", "f_0111",
"f_1000", "f_1001", "f_1010", "f_1011",
"f_1100", "f_1101", "f_1110", "f_1111"}
Hex(2) = {"f_0", "f_1", "f_2", "f_3",
"f_4", "f_5", "f_6", "f_7",
"f_8", "f_9", "f_A", "f_B",
"f_C", "f_D", "f_E", "f_F"}
Par(2). Painted And Rooted Cacti (PARC's), Parse Graphs for ZOL(2).
Ref(2). Reflective Extension of Logical Graphs (RefLog) for ZOL(2).
Eng(2). English renditions for ZOL(2).
Tra(2). Traditional syntax for ZOL(2).
Cub(2). Color in the nodes of a 2-cube to represent the proposition.
Ven(2). Shade in the cells of a 2-oval venn diagram in the usual way.
Ver(2). Point to the vertex in a lattice diagram that makes the point.
In order to apply the pragmatic theory of signs to any kind of setting
where signs are used to refer to objects, the first thing that we need
to do is to think about the sign relations that will be involved in it.
Suppose that we have settled on a triple <O, S, I>
that constitutes three sets of these descriptions:
O = object domain
S = sign domain
I = interpretant domain
An arbitrary sign relation L involving the relational domains O, S, I
is just any subset of their cartesian product, written L c OxSxI, and
this can be a pretty arbitrary thing indeed. But for logic's sake we
can narrow our focus to certain varieties of sign relations L c OxSxI,
most especially, those in which "it makes some kind of sense", to say
it intuitively, to pass from one sign to another while still thinking
about the same object. More strictly formulated, we may start out by
considering only those sign relations L c OxSxI whose 3-tuples of the
form <o, s, i> have the sign s and the interpretant sign i restricted
to being logically equivalent expressions, and where both s and i are
constrained to denoting the same logical object o. We may eventually
find reason to contemplate other varieties of sign relations, but the
special sort indicated will always form the logical core of our study.
Next time I will try to indicate the shape of a few concrete examples.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤