Squibs and Discussions 
Sethood and Situations 
T. E. Forster C. M. Rood 
In Situations and Attitudes (Barwise and Perry 1983) Barwise and Perry decide that 
meaning should be taken to be a triadic relation not a dyadic one. While there may 
be good reasons for deciding to procede on this basis, one of the reasons they give is 
definitely a bad one, and this is the principal subject of this note. 
On pages 222-23 they remark that if meaning is to be a dyadic relation it is nec- 
essary that the complement of a situation should--at least sometimes--be another 
situation. In the set theory that is the basis for their development--KPU--it is ele- 
mentary that the complement of a set is never a set. This compels the designers of 
situation semantics to make meaning a triadic relation as we will now explain. 
Barwise and Perry take individuals, properties, relations, and locations as prim- 
itives. A situation-type is a partial function from n-ary relations and n individuals to 
the set {0, 1} (p. 8). In modern situation-semantic parlance, this is often referred to as 
an infon, or (more precisely) a basic infon. An event, or course-of-events (coe), is a 
function from locations to situation-types. For example, the situation-type correspond- 
ing to a (real-world) situation in which a dog named Molly barks would be: 
(at I, barks, Molly, 1 / 
and one related coe might be: 
e = {(at I, barks, Molly, 1}, 
(at l', shouts at, Mr. Levine, Molly, 1), 
(at I", barks, Molly, O) } 
Consider the predicate SO (seeing option) on coes. In a given event, s, an individ- 
ual, a, classifies events according to what s/he sees and knows. That is: 
(SO, a, el, 1) E s if ea is compatible with what a sees and knows; 
(SO, a, e2, O) E s if e2 is incompatible with what a sees and knows. 
This is a partial classification of events; i.e., some events may be neither SO-yes nor 
SO-no. 
Further to this: 
• Definition 
In a given situation, s, an event, e, is a visual option for agent a if 
ISO, a,e, 1) E s 
• Definition 
Similarly, e is a visual alternative for a if it is not the case that 
(SO, a,e,O I E s 
Given s as above, let: 
Xvo = {e:ISO, a,e, 1) Es} 
= collection of events that are visual/seeing options for a in s. 
C) 1996 Association for Computational Linguistics 
Computational Linguistics Volume 22, Number 3 
Also, let: 
XNVO = {e: (SO, a,e,O) E s} 
= collection of events that a classifies as not being visual options. 
Then: 
XVA = collection of visual alternatives for a = XNvo. 
(In general, we cannot assume XNVO = Xvo.) 
An utterance, q~, determines a triple • = (d, c, q~) composed of a discourse situation, 
d, a speaker connection function, c, and the utterance, q~. 
Furthermore, our interpretation relation (a function from utterances of the above 
form to collections of events) is given as: 
\[~\] -= interpretation of ~ according to d and c = {e:d, c\[¢b~e holds}. 
The speaker connection function, c, (or anchor) grounds the individuals, relations, 
and locations mentioned in q~ to actual entities participating in the discourse situation, 
d. \[*~ is thus a binary relation, relating the utterance triple to the described situation, 
I¢~. Note that the discourse situation, d, is the situation in which ~b is uttered and thus 
is usually distinct from the described situation, I¢~1, except in cases of self-reflexive 
discourse. 
For example, if q~ = FIDO RAN, c(FIDO) \["FIDO" is mentioned\] = Fido \["Fido" 
is used\], and c(RAN) = 1 \[a location\], then if: 
(l, ran, Fido, 1) E e 
we have e E I¢~1. 
There is a problem with this analysis that leads Barwise and Perry to seek a 
representation of mental states and events with which to augment the interpretation 
relation. The problem involves a distinction Barwise and Perry make between epis- 
temic and non-epistemic perception. Attitudinal reports involving the phrase "see 
that" followed by a finite complement involve epistemic perception--that is, they 
yield information about the inference an agent has performed after seeing a given coe 
or situation (p. 207). The problem comes about when Barwise and Perry attempt to 
characterize attitude reports involving "see that" in terms of the relation SO. 
On pages 209-11 Barwise and Perry claim: 
a sees that ~ ~ {e : not d, c~e} c XNvo(*) 
i.e., those events not in the interpretation of ~b must be classified as SO-no. They give 
the following proof, on page 211. 
Proof 
"A situation e is one where a sees that ~ if q~ holds in each of a's visual alternatives at 
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the appropriate location, I." That is: 
a sees that ~ ~ XVA C_ ~ 
and since XVA C_ ~ ~ ~1 C_ XNVO (taking complements), we obtain the result. 
This yields the following situational analysis of attitudinal reports involving epis- 
temic perception. Given an utterance: 
0. := a SAW THAT ¢~ 
in order for 0. to describe an event, e, we use (,) to obtain that we must have at 
l = c(SAW), for every event, e~, either: 
el E I~1 
or: 
(l, SO, a, el,0) E e. 
The fact that any SO-no event must be classified as such by the event e (the event 
corresponding to the attitude report) means that if we view e as a collection of infons, 
we will have: 
\[el >_ IXNvo\[ 
and by a result above, IXNVOl >_ -~. 
It is Barwise and Perry's contention (p. 222) that I4)~ is a proper class, therefore e 
is as well. Consider the utterance: 
0.1 := JOE SAW THAT JACKIE WAS BITING MOLLY. 
Barwise and Perry argue that 
there is a proper class of events el in which Jackie was not biting 
Molly, events that must be classified with SO-no. But then \[the event\] 
e required to classify Joe's visual state must be a proper class. (p. 222) 
Thus such events cannot, for example, be constituents of other situations. In particular, 
iterated (or embedded) attitude reports cannot be handled in this framework. A report 
such as: 
0.2 := JOHN SAW THAT JOE SAW THAT JACKIE WAS BITING MOLLY 
would require that the event, e, classifying Joe's visual state be a constituent of 0.2's 
interpretation, \[~21. This is because the interpretation relation, d, c~G2~e holds: intu- 
itively, the putative event corresponding to the situation described in 0" 2 would have 
to include e since Joe's visual state in fact comprises the complement of the outer "see 
that" clause. Yet e is a proper class and so we cannot have e E ~G21 as we require. 
This can be rectified by adopting as a set-theoretic basis a set theory in which 
the complement of a set is always a set. In this case, the analysis proceeds as before, 
saving that the collection ~ff)~ (as above) is now a set. With the collection XNVO no 
longer formally constrained to being a class, arguments of the type rife throughout 
(Barwise and Perry 1983) can be lodged to illustrate XNvO'S "set-ness," as well as that of 
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the interpretations of utterances such as cr 1. Thus the situational analysis of attitudinal 
reports extends to iterated reports such as or2 without violation of set membership 
dicta. 
Whatever reasons caused Barwise and Perry to desire a set theory with ur-elements 
should presumably still be respected, so if we can find a consistent set theory with 
ur-elements and a universal set, the outlook will be a lot brighter. Fortunately there is 
such a system, the Jensen-Quine system of set theory known as NFU. For more on this 
see Holmes (1994, 1996). Of course, an easy consequence of an axiom of complemen- 
tation such as we have in NFU is the negation of the axiom of foundation. Barwise 
has elsewhere (1984) argued that we should not regard the axiom of foundation as 
essential. 
References 
Barwise J. 1984. Situations, sets and the 
axiom of foundation. In Paris, Wilkie, and 
Wilmers, editors, Logic Colloquium '84, 
pages 21-36, North-Holland. 
Barwise, J., and J. Perry. 1983. Situations and 
Attitudes. MIT Press, Cambridge, MA. 
Holmes, M. R. 1994. The set theoretical 
program of Quine succeeded (but nobody 
noticed). Modern Logic, pages 1-47. 
Holmes M. Randall. 1996. Naieve set theory 
with a universal set. Unpublished, 
available on the WWW at 
http: / / math.idb su.edu / faculty / holmes.html 
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