Information Technology Reference
In-Depth Information
10 What is an Information State?
This is also a bit of a digression (no pun intended). Routley-Meyer, Urquhart,
and Fine, all have in their semantics a set of
elements
corresponding to Kripke's
possible worlds in his semantics for modal logic (often called “possible worlds
semantics”). But these elements cannot be taken to be possible worlds, for they
are often incomplete and/or inconsistent. Thus, for some element
a
and sentence
A
we may have neither
a
|
=
A
nor
a
|
=
∼
A
, and for another sentence we may
have both
a
A
.
Routley-Meyer coined the name “set ups” for their elements. Urquhart used
the term “pieces of information,” and Fine used the term “theories.” We have
tended to use the term “information state.”
11
This is clearly an abstraction, but
a concrete way to think of it is as the state of a storage system in a computer.
This can be visualized for an antique computer as the setting of switches (either
on or off), or for a hard drive as changes in direction of the magnetic field from
place to place. No matter the physical method of storage, an information state
may be thought of as a finite sequence of bits, either 1 or 0. Propositions can
be thought of as sets of information states, and each proposition
P
is true of
false in a given information state
a
depending on whether
a
|
=
A
and
a
|
=
∼
P
,and
in principle, this goes back to Shannon. It is related to Carnap and his state
descriptions - see for example Dunn (2001a). In this setting the Routley-Meyer
valuation clause
∈
P
or
a/
∈
(v
∨
)
x
|
=
A
∨
B
iff
x
|
=
A
or
x
|
=
B
makes perfect sense.
But for a more ordinary conception of an information state the left-to-right
direction is problematic. I remember that I left my keys upstairs on the dresser,
or in the basement on the workbench, but I don't remember which. Or suppose
I am about to throw a coin. I have the information that it will turn up heads or
tails, but I do not have the information as to which. Or suppose the dog knows
that his master took either the left fork of the path or the right fork, but does
not know which (he hasn't yet sniffed). Or in playing the game
Clue
, figure out
that that the murder was committed by Miss Scarlet with a knife in the study,
or by Professor Plum with a candlestick in the dining room, etc.
Urquhart, calling the elements of his semantics “pieces of information,” runs
head on into this problem. Fine, calling his elements “theories” would seem
to also, for clearly theories can contain disjunctions without containing either
disjunct (look at the theories above about my keys, etc.). But Fine has a way
out. He has special kinds of theories. Besides the set
T
of ordinary theories
he has the subset
S
“of all theories that contain a disjunct of any contained
11
But back in the old days of Dunn (1976), I used the term “situation.” And Mares
(2004) with his “situated semantics” continues to use the term “situation,” partly to
build an alliance with the Barwise-Perry Situation Theory. Situations would seem
to provide plausible terminology for “situated relevance”: situation
b
is relevant to
situation
c
in the context of situation
a
.
