Solving Some Persistent Presupposition tProblems 
Robert E. MERCER.* 
Department of Computer Science 
Middlesex College 
University of Western Ontario 
London, Ontario, Canada 
N6A 5B7 
Abstract 
/S0aanes 1979/provides some counterexamples to the theory of nat- 
ural language presuppositions that is presented in /Gazdar 1979/. 
/Soames 1982/ provides a theory which explains these eounterex- 
amples. /Mercer 1987/ rejects the solution found in/Soames 1982/ 
leaving these eounterexamples unexplained. By reappraising these in- 
sightful counterexamples, the inferential theory for natural language 
presuppositions described in/Mercer 1987, 1988/gives a simple and 
straightforward explanation for the presupposiitional nature of these 
sentences. 
1 Introduction 
/Soames 1979/ provides some intriguing counterexamples to the 
method for deriving natural language presuppositions presented in 
/Gazdar 1979/. A proposed modification to Gazdar~s method 
(/Landman 1981/) which attempts to solve the problem exhibited 
by these couuterexamples by introducing extra clausal implieatures 
"has been effectively argued against in/Soames 1982/. 
Motivated by the lack of explanation for these reasonably simple 
counterexamples, /Soames 1982/ constructs a mechanism that de- 
rives presuppositions that is a superset of the approaches suggested 
by/Gazdax 1979/and/Karttunen and Peters 1979/. /Mercer 1987/ 
contains methodological and empirical arguments against Soames' 
approach to the derivation of natural language presuppositions. 
This paper presents a reappraisal of some of the insightful coun- 
terexamples to Gazdar's method given in /Soames 1982/. Given 
an appropriate representation of the sentences in question~ the de- 
fault logic approach to natural language presuppositions described in 
/Mercer 1987, 1988/gives a simple and straightforward explanation 
for the presuppositional nature of these sentences. 
2 General Background 
There has been a long history of attempts to define methods that 
would produce the presuppositions of a sentence. The default logic 
approach that is highlighted here follows the general framework set 
out in /Gazdar 1979/. One feature of this framework is that the 
speaker is governed by Grice's Principle of Cooperative Conversation. 
Assuming these general guidelines allows a competence model of the 
hearer's interpretation to generate the appropriate presuppositions of 
sentences with the forms 'a or b' and 'if a then b'. Details of this 
process is given later. 
2.1 Linguistic Presuppositions 
Being implied by a natural language sentence and the natural (or 
preferred) interpretation of its simple negation is the primary qual- 
ity that qualifies an inference as a presupposition. This evaluation 
*This ~esearch was partially supported by NSERC grants A7642 (to It. Reiter) 
and A3039 (to P. C. Gilmore). 
420 
of inferences is called the negation test. Presuppositions are gener- 
ated from lexical and syntactic contexts. Those contexts which pass 
the negation test can be termed presuppositional environments. Sen- 
tences (1)-(2) demonstrate some prototypical examples of presuppo- 
sitions produced by the presuppositional enviromnents, factive verbs 
and definitions of words. In each of these examples tim truth of the 
affirmative a-sentence always implies the truth of the c-sentence, and 
the truth of the negative b-sentence normally implies the truth of the 
c-sentence. 
(1) a. 
b. 
C. 
Mary is surprised that Fred left. 
Mary is not surprised that Fred left. 
Fred left. 
(2) a. My cousin is a bachelor. 
b. My cousin is not a bachelor. 
c. My cousin is a male adult. 
2.2 Projection Rule Procedures 
The procedures for deriving presuppositions of complex sentences 
prior to/Mercer 1987, 1988/that have received most attention are 
the ones based on the projection rule. These include/Karttunen 1973, 
1974/~ /Karttuuen and Peters 1975~ \]979/~ /Gazdar 1979/, and 
/Soames 1979~ 1982/. The details of these theories are not important. 
What is of importance is the linguistic basis for these theories. 
Crucial to any theory, of natural language presuppositions is the 
concept of a presuppositional environment. These lexical or syntactic 
enviromnents generate inferences, which are called presuppositions, 
whether they are in the scope of a negation or not. In addition to 
tl~e concept of presuppositional environments~ what is common to all 
the linguistic theories is the notion of a projection rule which projects 
the generated inferences as presuppositions of the sentence. The naive 
projection rule proposed in /Langendoen and Savin 1971/takes all 
the presuppositions from all the presuppositional environments con- 
rained in the sentence and projects them as presuppositions of the 
sentence. 
Although the modifications to this simplistic rule differ (see/Kart- 
tunes 1973, 1974/, /Karttunen and Peters 1975, 1979/, /Gaz- 
dar 1979/, and \]Soames 1979, 1982/), a common theme is that pre- 
suppositions are connected with surface phenomena. Although the 
methods differ in the importance that the semantic representation 
plays in the derivation of the presuppositions, without exception the 
potential presuppositions that are candidates for the (modified) pro- 
jection rule are generated because the presuppositional environment 
exists in the surface form of the sentence; 
2.3 A Default Logic Approach 
The approach presented in /Mercer and Reiter 1982/ and /Mer- 
cer 1987~ 1988/has a number of distinguishing features. 
1. The method is based on inferencing in a logical system, although 
the logic is not a classical one. 
2. The me~hod uses semantic representations of the naturM la.n- 
guage sentence. Iu the case of 'if a then b' the semantic repre- 
sentation that is nsed directly is a derived representation (a D b 
can be derived from a > b, where > is StalnM¢er's connective for 
3. All presuppositional environments that generate presuppositions 
must be within the scope of a negatiou eil:lter in the represen.. 
taUon el' the sentence or some logical for:m derived from tlfis 
representation. 
ilow the method interact:~ with sentential adverbs is the main 
theme of this paper. The definition of presupposition and the working 
of the inference procedure in /Mercer 1987, 198'8/ solves the seeping 
problenrs caused by the interaction of negation and other environ- 
ments. In the discussion of sententiM adverbs it will be shown that 
the normal ~mntence-seope for negation is circunwented in certain 
circamst;utc(:s. This circumvention of the normal rule explains the 
presuppositi, utal behaviour of the sentential adverb environment. 
2.3.1 Log.eal tEepresentatlon of 
Pre.quppoMtions rising Default 
R.ulos 
A no,'mal default ~*ule is a rule of inference denoted 
fl(Y) 
where a(Y) mM fl(x') are a.1\] first order formulae whose fl'ee variables 
are among those of .~ = xl,...,x,,. Intnitively, a default rule can 
be interpreted as: For all individuals xi .... ,xm, if the prerequisite 
t~(Y) is belie,rod I and if fl(,~') is consistent with what is believed, then 
the consequent fl(.~°) nray be conjectured. A ~lormal default theory 
is a set of l\[rst order lbrnrulae together with a set of normal de- 
faults. A fized point of a normal default theory is the deductive 
closure of tire set eomprised of the first order fornrulac and some 
maximal set of eonsequents that are consistent with the fixed point. 
The CONSIs'QUENTS'{D} is the set of all conseqaents of the default 
rules in the default thnory. 
For the purposes of this paper, I will change slightly the interpre- 
tation of the default rule to mean: if the speM¢er says 'a(~')' and 
fl(Y) is consistent with the heater's knowledge base, KBH, then the 
hearer can conjecture fl(,~;). it is not M)solutely clear what the verb 
says means (u' how it should be represented. For the purposes of this 
1raper I only require those notions first presented in/Grice 1975/un- 
der the title Principle of Cooperative Conversation and formMized in 
/Gazdm" 1.979/. Under Ga:zdar's interpretation of Grice's maxims the 
speaker is e(,mmitted to the truth of u, the sentence that he utters. 
Therefore the speaker knows u. The conversational approach that I 
take views the contrihntion of a speaker's ntterance u as the addition 
of Ksu to 1(t111 along with other conversational intbrmation wldch 
is detailed in section 2.3.2. The meaning of the utterance is then a 
function of the inierencing process on I~Bl-1 U {I<su }. 
The default rules require some extra informa*:ion to guard against 
misuse of the default rules. This information is a conjunct in the 
prerequisite of the default rule. Except for this technical aspect this 
extra intbrmation plays no role. Since it creates long default rules, 
i have tell it out of all the examples. For further details see/Mer- 
cer /.987/. 
Whenever the discussion concerns the default logic approach, I will 
assnme that the speaker's utterance has undergone the first phase of 
the interpretation process which generates a semantic representation 
(logical form) of the sentence uttered. This ,;entantic representation 
The verb believe sholdd be t~kea to lm?&lt first order dctiw~ble or conjectured 
from the default theory. 
will be a well-formed sentence in a first order $4 modal language 
containing a countably intinite set of predicate syntbols, constant 
symbols, and variable symbols, plus the logical symbols A, V, D, -, 
Ks, ~nd Ps. The last two symbols, called modal operators, are to 
be interpreted as 'the speaker knows that' and 'for all the speaker 
knows, it is possible that', respectively. Although there is no general 
method known to generate this representation, some generM rules 
(:an be followed. Any sentence with an explicit negation is translated 
into the widely seeped negation of its affirmative counterpart. Any 
compound sentence is mapped clause by clause into a logical form, 
each clause being treated as a sentence. 
2.3.2 Deriving Presuppositions in 
Complex Sentences 
The concept discussed herein -- using default logic to derive presup- 
positions -- is strongly influenced by Gazdar's method. I will present 
the representation of presuppositions in following sections with lit- 
tle explanation. For a complete discussion of how presul)postions 
are represented by default rules in a default theory together with 
how default logic proof theory captures Gazdar's idea of presupposi- 
tions being consistent with a context see/Mercer and Reiter 1982/or 
/Mercer 1987/. Another influence is the use of clausal implicatnres in 
connection with deriving presuppositions fl'om complex sentences, tu 
the default logic approach the clausal implicatures are used to control 
the division of the original theory into its first order cases. 
The clausal implicatures are derived fi'om the natural language 
sentence according to Gaz, dar's formal treatment of Grice's converss 
tional principles (/Griee 1975/). The sentence uttered by a speaker 
commits the speaker not only to the truth of the sentelme but also 
to the possibility of its clauses (its parts). So in tlm case of the 
speaker uttering 'A or B' or 'if A then B', unless tlmre is background 
knowledge or there are linguistic reasons to prevent it, the speaker b; 
committed to PsA, Ps-,A, PsB, aud Ps,'~B. These implicatures will 
provide the means to restrict the division of the theory representing 
the utterance into its cases. 
Becmtse default logic proof theory does )tot display any analogue 
to the law of the excluded middle (the antecedents of tim default: 
rules nrust be provable and there is no equivalent to the deduction 
theorem) and because presuppositions do arise from the clauses of 
complex sentences, some form of analysis by eases is required. Since 
a statement is provable in a case anMysis only if it is provable in all 
cases, the choice of cases is critical. As in the case of a tirst order 
theory, too few cases would allow inappropriate statenmuts to Ire 
proved. In addition because of the non-monotonic nature of default 
logic, having too many casts could prevent al)propriate statements 
being proved. 
In general the choice of cases must reflect two principles. Since 
the case analysis is a proof theoretic analogue of the model theoretic 
law of the excluded middle, each ease must completely determine 
the truth values of each of the disjunets found in the statement to 
which case analysis is being applied. Also, since the case analysis is 
justified solely on linguistic grounds (see /Mercer 1987/ for further 
discussion), the cases must reflect this linguistic situation. 3'o justify 
a. case, the possibility of the statement that distinguishes the case 
must 1re provable t¥om the original default theory. Since none of the 
modM statements take part in the proofs, they are left out of the 
cases. An example should clarify these ideas. 
Example 
Suppose the sentence 'A or B' is uttered. '\]?he default theory 
repre.senting this utterance would be 
T = {Ks(A V B), PsA, Ps-,A, PsB, Ps-,B, 
al, • • •, cx,~, 61,.. ,, ~/~} 
421 
where ax,..., a, represent the appropriate first order state- 
ments and $1,. •., ~n represent the appropriate default rules. 
Since A A-~B and -~A A B completely determine (that is, de- 
termine the truth values of both) A and B, and since the 
statements Ps(A ^ -~B) and Ps('~A A B) can be derived, 
A ^ -~B and -~A ^ B distinguish the two cases. Note that 
although PsA, Ps'~A, PsB, Ps'~B are all derivable, none of 
A, -~A, B, -~B are candidates for distinguishing a case be- 
cause, individually, none of them completely determine the 
truth values of both A and B. 
Ilence the two cases of the original theory, T, are 
Tc~s~x = {A A "nB,al ..... an, 61 ..... 6n} 
Tease", = {~A ^ B, al,..., an, ~'1, • .., ~',~} 
The simple negated sentence, an example of which is presented in 
section 2.3.1, is just a special instance of the case analysis procedure. 
In the simple negated sentence, -~X (which is represented as Ks-~X), 
the possibility of the only case (distinguished by -~X) can be proved 
using the utterance and the theorem ~- Ks~X F- Ps-~X. 
2.3.3 A Proof-Theoretlc Definition of 
Presuppositions 
Definition 1 A sentence ex is a presupposition of an utterance u, 
represented by the default theories Auc~.~t ..... Aua .... 2, if and only 
/f A,c~ , ~-A a for all i and a e Th(CONSEQUENTS{D}), but 
Au ~/ o~ and Au \[/A .,~3. 
This definition can be loosely paraphrased as: ifa is in the logical 
closure of the default consequents and is provable from the utterance, 
and all proofs require the invocation of a default rule and in the case 
of multiple extension default theories, a is in all extensions, then a 
is a presupposition of the utterance. 
2.4 Important Differences 
The previous approaches which have been mentioned above rely on 
two ideas. Firstly, presuppositions are generated from positive and 
negative presuppositional environments, if these environments occur 
in the surface sentence. Secondly, a number of different methods, 
collectively called projection methods, are used to screen out those 
potential presuppositions which are not to be projected. A brief 
description of Soames' method is given in section 4.1. 
The default logic theory described in detail in/Mercer 1987, 1988/ 
approaches the problem of presupposition-generation from the level of 
logical representation. Presuppositions are generated from the logical 
representation if negated presuppositional environments occur in the 
logical representation of the natural language sentence or some logi- 
cal form which can be derived from this representation. Malay of the 
results that the modified projection methods achieve are just proof 
theoretic results in the default logic approach to natural language 
~For purposes of this definition, the only defaults in each Auco,o i a~e the 
presupposition generating defaults. In reality the default theory would contain 
many other kinds of defaults. The definition would have to be changed so that 
the proof of c~, requires the invocation of a presupposition generating default, 
and that a E Th(CONSEQUENTS{D'}), where D' is the set of presupposition 
generating defaults 
~All of the examples presented in this paper deal with default theories having 
single extensions. In those theories which have multiple extensions, some way 
of stating that a presupposition is in all extensions is required. Since extensions 
of normal default theories are orthogonal, if An has multiple extensions then 
there exists a sentence fl such that Au I-A fl and Au V-a ~/?. I will call this 
situation being split along the fl-dimensiom If the extensions do not split along 
the ~-dimension then either ~ is in all extensions or a is in no extension. So if 
Au f-a ~ (which means that at least one extension contains ~) and Au V/a ~a 
(which means that no extension contains ~a, which means that the extensions do 
not split on the a-dimension) then ~ is in all extensions. 
422 
presuppositions. In addition, once the logical representation of sen- 
tential adverbs is presented, it will be shown that the solution to the 
problem of presuppositions derived from sentential adverbs is again 
obtained in the default logic approach without any modifications. 
3 Sentential Adverbs 
The two sentential adverbs that will be presented are those found in 
the examples given in/Soames 1982/: 'too' and 'again'. Becanse one 
of the defining properties of a presuppositional environment is indio 
caring positive to the negation test 4, I will first look at each when 
there is a negation present. The interesting property displayed by sen- 
tential adverbs is that in addition to any interaction between negation 
and the underlying form, there is also an interaction between nega- 
tion and the adverb. This interaction can be captured in two different 
logical representations. 
The sentential adverbs have the added complication that they can 
take any part of the sentence as their focus of the adverb. The focus 
of the adverb will be capitalized. Although the verb of the sentence 
can be focussed, a presentation of this particular focus would require 
an event-based representation. I do not discuss this focus in the 
following. However, it, too, would behave analogously. 
3.1 Too 
The representations of 'kick too' are shown in (3) and (4). These 
two representations convey the different foci of the adverb, 'too', the 
subject and the object of 'kick', respectively. I will be only interested 
in the representation which focuses on the subject, that is (3). The 
explanation for presuppositions that arise from the adverb focussing 
on the object is similar to the discussion presented below. 
(3) ~/xVy.KICK-SUBJ-TOO(x, y) =- 
KICK(x, y) ^ ~z.KfCK(z, y) A x # z 
(4) VxVy.KICK-OBJ-TOO(x,y) =- 
KICE(x, y) ^ 3~.ICICK(~, ~) ^ y # z 
Sentential adverbs have a most peculiar attribute when they inter- 
act with natural language negation. The adverb can be either inside 
or outside the scope of the negation. Sentences (5) and (6) point out 
the two possible interpretations in the case of 'too'. One particularly 
interesting phenomenon is that all of the possible scopes of the nega- 
tion and the adverb may not occur in surface form. For instance, 
(6) would normally be uttered as 'BILL didn't kick the ball, either.'. 
I will use the incorrect surface form in the examples, however. The 
italicized portions of the sentences indicate the portion which is in 
the scope of 'too'. (5) is to be interpreted as: Although someone else 
kicked the ball, Bill didn't. (6) is to be interpreted as: Both Bill and 
someone else did not kick the ball. 
(5) BILL didn't kick the ball, too. 
(6) BILL didn't kick the ball, too. 
The representations for the unnegated 'BILL kicked the ball, too.' 
and the sentences (5) and (6) are shown in (7)-(9), respectively. As 
proposed in /Kempson 1975/, /Wilson 1975/, and implemented in 
/Mercer 1987/, the representation of the simple negation of the sen- 
tence 'BILL kicked the ball, too.' is just the wide-scoped negation 
as shown in (8). I have shown the right-hand side equivalents of the 
appropriate representations so that I can contrast the two different 
uegatlons. 
(7) KICK(Bill, ball) A 3x.KICK(x, ball) A x ~ Bill 
4A positive indication to the negation test means that a sentence, 8, containing 
the purported presuppositionai environment and the preferred interpretation of 
not S both have the same inferences arising from the environment in question. 
(8) -,\[KICIt( Bill, ball) A -lx.KIClf(x, ball) A x ¢ Bill\] 
(9) -~KIG'l( ( Bill, ball) A Hx...~KICK (x, ball) A x ~ Bill 
What is important for tile presuppositional analysis is that only 
(8) can be a candidate for the negation test. One of the prerequi- 
sites of this test is that the supposed presuppositional environment is 
within the scope of the logical negation in the logical representation 
of the sentence. The logical representation of (9) does not meet this 
requirement. 
3.2 Agai a 
The situation for the sententia| adverb, 'again', is somewhat similar 
to that described above for 'too'. The adverb can be inside or outside 
the scope of the negation. Accordingty~ the adverbs found in (10) and 
(11) are the presupl)ositional and non-presuppositional enviromnents 
with respect to the positive sentence 'Fred called again,'. (10) is to 
be interpreted as: At some time in the past Fred called and during 
some interwl of time which is important to the context in which 
the sentence is uttered, Fred didn't call. (11) is to be the following 
interpretation: At some time in the past Fred didn't call and during 
some interval of time which is important to the context in which tile 
sentence is u~tered, Fred didn't call. 
(10) I,'RED didn't call again. 
(11) FRED di&~'t call again. 
Th.e representation for 'call, again' is shown in (12) 5. 
(12) VxVyVz.CALL-HUBJ~A GAIN(x, y, z) =- 
CALL(x, y, z) A 3tl. CALL(x, y, tt) A tl < z 
The representations for the unuegated 'FRED called again.' and the 
sentences (1(t) and (11) are shown in (13)-(15), respectively. As in 
the case of 'too', the representation of the simple negation of the 
sentence 'Fb~ED called again.' is just the wide-scoped negation as 
shown in (1+1). i have shown the right~hand side equiwdeuts of the 
appropriate representations so that I can contrast the two difihrent 
negations. 
(13) CALL(Fred, you, t) A :3tj .CALL(16~d, you, h) A tl < t 
(1.4) -,\[ CAL t,(1,Yed, you, t) A i~tt. CAI, L( Ft~d, you, 11) A t 1 < t\] 
(15) -,CALL( I;Yed, you, t) h ~tl.'-,CALL( Fred, you, h) A tl < t 
As in the case for 'too', the only representation of 'again' that 
sanctions the use of presuppositioual machinery is (14) s. 
4 Two Approaches to the Problem of Sen-~ 
tential Adverbs 
Now I ca~ turn to these sententiM adverbs occurring in more com- 
plex situations~ in particular, examples similar to those provided in 
/Soaanes 1982/. The two examples shown in (1.6) and (17) are the 
kinds of situations which prove difficult for all projection methods. 
(16) if JOHN kicked the ball, then BILL kicked the ball, too. 
(17) If Fred called yesterday, then he will call again, 
SThis representation conveys only oac foci of the adverb, 'again', in this c~e, 
the subject. The object of 'calP, which in this case weald have to be recovered 
from cow, textual cues (it would pt'obably be 'yon' or 'us', though it could bc a 
ihird party) can be focussed as well. Since the discussion is similar to that given 
for ~too ~, I will omit it. 
SThis is of coarse with cespect to the ~eutence represented by (13). 
4.1 Soames ) Approach 
Tile method proposed in /Soames (1982)/ is based upon the belief 
that the two major competing strategies for determining presupposi- 
tions (/Karttunen and Peters 1979/and/Gazdar 1979/) succeed in 
those situations in which the other one fails. 7 Tile proposed solution 
is to synthesize the two filtering strategies so that all the unwanted 
potential presuppositions are screened out. 
The synthesis is performed in the following manner. First the po- 
tentialpresuppositionsofthe sentence are computed. Essentially, the 
potential presuppositions are all of tile presuppositions of the indi- 
vidual clauses of the sentence if the clauses were in isolation. The 
remaining potential presuppositions are those potential presupposi- 
tions which are not contextually or eonversationMly cancelled. This 
step is basically Gazdar~s method for generating the presuppositions 
of the sentence. The next step is to use these remaining potential 
presuppositions in the projection phase which is basically the one 
proposed by Karttunen and Peters. 
Since all of the examples that Mlow deal only with qf... then' 
sentences, I will provide only the projection rule for this kind of 
sentence. 8 
If S :='If A then B', then the actual presuppositions of S are 
those entailed by 
A P ^ (Ar 79 B y) 
where eP represents the actual presupposition of ¢. 
A further aspect of this rule is that if A T D B P is true only for truth- 
conditional reasons or is a logically valid statement, then this part 
of the conjunct is ignored. Otherwise, the 'A T D' is dropped giviug 
A P A B P as tlle presupposition of the sentence 5'. 
This projection method can be applied to a variety of examples. 
Since I am concerned only with the characteristics of the presup- 
positional environment 'too' in these examples only those potential 
presuppositions that are relevant will be mentioned in the anMysis. 
(16) has the following properties. 
No potential presuppositions are derived from the an- 
tecedent clause. 
A T 79 B P = John kicked the ball D somebody (~ Bill) 
kicked the ball 
Since A T D B p is logically valid it is ignored, tIence (16) 
has no actual presuppositions. 
Similar analyses give no presupposition for (18) and the pre,mpposi.- 
tion 'Somebody (~ John) kicked the ball.' for (19). 
(18) BILL kicked the ball, too, if JOIIN kicked the ball. 
(19) If JOIIN kicked the ball too, then BILL kicked the ball 
Ia order to generate no presuppositions for (20), /So~mes 1979/ 
requires an extra rule and a somewhat suspect method of interpreta- 
tion. A description of the extra rule is not needed here. tiowever, a 
quick look at the accompanying method of interpretation is of some 
importance. In order for the extra rule to work properly, the clause 
B in the sentence 'BifA' must tirst be interpreted am an assertion. 
This error is undone when the 'if A' portion is heard. But what is 
important is the appropriate presuppositions have been c;mcelled by 
this point, tIowever, it seems that stress patterns on the llnal word 
of B when uttered as a sentence and when uttered as the lirst clause 
of 'BifA' differ. Hence no hearer would interpret B as an asser- 
tion. Without this peculiar interpretation, Soames' method cannot 
correctly generate the presuppositions for (20). 
(20) BILL ldcked the ball, if JOIIN kicked the ball ~oo. 
~/Mercer 1987/ shows th~tt there are situations not covered ly the anion ot 
thcsc two methods. 
aThis rule is a slightly simplified version of the one given in/So,.mcs 1982/. It 
is sufficient for this discussion. 
423 
4.2 A Default Logic Approach 
The default rule schemata which capture the presuppositionai in- 
ferences for the adverbs, 'too' and 'again', are (21) and (22), re- 
spectively. In the case of 'kick too' and 'call again' the appropriate 
instances of these schemata are shown in (23) and (24), respectively. 
(21) "~\[¢(x,y) A3z.¢(z,y)Ax#z\]:3Z.¢(z,y)Ax #z 
3z.¢(z, y) A x # 
(22) J¢(x, y, t) A 3t'.¢(x, y, t') A t < t'\] : 3t'.¢(x, y, t') ^ t! <~t 
(23) 
3t'.¢(x,y,t') A t t < t 
-.KICK-SUBJ- TOO(x.y) : 3z.KICK(z,y) /~ x # z 
3z.KICK(z, y) h x # z 
-,CALL-SUBJ-AGAIN(x,y,t) : 3t'.CALL(x,y,t') ^ t' < t 
(24) 3t'. CALL(x, y, t') A t' < t 
Given simple statements such as those in (25) and (26) the pre- 
ferred interpretations can be derived from the representation of the 
sentence and the appropriate default rules. I have shown the rep- 
resentation for (25) in (27). The preferred interpretation of (25) is 
shown in (28). Similar representations can be derived for the pre- 
ferred interpretation of (26). 
(25) Bill didn't kick the ball, too. (In the sense of (5).) 
(26) Fred didn't call again. (In the sense of (10).) 
(27) -,KICK(Bill, ball) V Vz.-~KICK(z, ball) v Bill = z 
(28) -,KICK(Bill, ball) A 3z.KICK(z, bail) A Bill # z 
Each of the sentences (16)-(20) requires a case analysis. The rep- 
resentation of 'if a then b' is not equivalent to a D b. However 
a D b can be derived fi'om standard representations for 'if a then 
b' such as Stalnaker's conditional logic representation, a > b (/Stal- 
naker 1968/). The theory presented in/Mercer 1987, 1988/ defines 
presuppositions as inferences derivable from a theory which includes 
the representation of the sentence. Therefore the logical form a D b 
will be available to the deductive machinery. For any sentence of the 
form 'if a then b,, the KBH U {Ksu} will be 
{Zs(a > b), 'appropriate default rules'} 
and since Ks(a D b) is derivable from Ks(a > b) and since Ks(a D b) 
is equivalent to Ks(~ayb) the two cases determined by the algorithm 
given in section 2.3.2 are 
{ a A b, 'appropriate default rules'} and 
{,a ^ -,b, 'appropriate default rules'}. 
The complexity arises in the case of sentential adverbs being in ei- 
ther the antecedent or consequent clause of the 'if... then' sentences 
under investigation because the negation which appears in one of the 
cases can be done in two possible ways wheat a sentential adverb is 
contained in the clause being negated. If the negation of the conse- 
quent clause does not put the sentential adverb in the scope of the 
negation, the default rule which generates the presupposition cannot 
be used. The case --a ^ -,b does not infer the presupposition. Conse- 
quently, the case analysis cannot generate the presupposition as an 
inference from the sentence. 
How is the method of negation justified? Two assumptions must 
be made. Firstly, the antecedent of an 'if ... then' sentence is logi- 
cally prior to the consequent. This logical assymetry can be derived 
fi'om Stainaker's analysis, or the cause and effect relationship that is 
conveyed by this sentence schema. Secondly,/Stalnaker 1973/gives 
an argument that 'if... then' sentences are to be interpreted in a 
manner that is similar to conjunctive sentences. Stainaker's view of 
conjunctions is that the second sentence is affected by the presence 
of the first sentence. I will loosely interpret this to include the way 
the sentence is represented. Therefore if there is a sentential adverb 
in the second conjunct, it should interact with any negations in such 
a way as to have the same interpretation as in the first clause. For 
example, (29) should have the representation given in (30). 
(29) JOIIN didn't kick the ball and BILL didn't kick the ball, too. 
(30) -,KICK(John, ball) A -,KICK(Bill, ball)A 
3z.-,KICK ( z, ball) A Bill # z 
Itowever, in (31.) since the first clause does not contain any negation 
that would affect the interpretation of the negation in the second 
clause, the negation in the second clause would follow the standard 
clanse-scoping negation rule. The representation for (31) is given in 
(32). This representation together with the appropriate default rule 
then produces the presupposition 'Somebody (~- Bill) did not kick the 
ball.'. 
(31) Today is not Sunday and BILL didn't kick the ball, too. 
(32) -1 Today is Sunday A ~\[ KICI( ( Bill, ball) A 
3z.KICK(z, ball) A Bill ~ z\] 
For any sentence of the form 'ira then b', the two cases determined 
by the algorithm given in section 2.3.2 are a A b and ~a A -,b. The 
representations for the second case for each of the sentences (16), 
(18), (19), and (20) are given in (33)-(36), respectively. The nega- 
tion in (33) is within the scope of the adverb because the adverb 
occurs in the consequent and because the antecedent is logically (azM 
conversationally) prior to the consequent. Therefore the scoping is 
dictated by that in the antecedent clause. Similar analyses can be 
given for (34) and (36). In (34) the adverb occurs in the consequent, 
hence the scoping is dictated by the logicMly prior antecedent, in 
(36) the adverb is in the antecedent, but because the consequent is 
coaversationMly prior to the antecedent, it dictates the scoping of 
the negation in the antecedent. In all of these cases the scope of 
the negation prevents the use of the presuppositionai default rnles 
to derive the presupposition that would be derived from the clause 
if it appeared in isolation. Only in (35) does the logically and con- 
versationaily prior antecedent contain the adverb. The scope of the 
negation is therefore determined by the normal scoping rule, hence 
the scope of the negation is the whole clause placing the adverb inside 
the scope of the negation, and giving the appropriate presupposition. 
(33) -,KICK(John, ball) A ~KICK ( Biil, ball) A 
3z.',KICK(z, ball) A Bill ~: z 
(34) -,KICK(John, ball) A -,KICK(Bill, ball) A 
-\]z.',KICK(z, ball) A Bill # z 
(35) -,\[KiCK(John, ball) A'~z.KICK ( z, ball) A John # z\] A 
",KICK(Bill, ball) 
(36) -,KICK(John, ball) h ~z.-,KICK(z, ball) A John # z ^ 
-,KICK ( Bill, ball) 
5 Conclusions 
/Soames 1979/ provides some counterexamples to the method to 
derive natarai language presuppositions that is presented in /Gaz- 
dar 1979/. To circumvent this problem, /Landman 1981/ intro- 
duces extra clausal implicatures into the method proposed in/Gaz- 
dar 1979/. This proposal has been effectively argued against in 
/Soames 1982/. 
/Soaznes 1982/ has enlarged the set of counterexamples found in 
/Soames 1979/. Motivated by the lack of explanation for these rea- 
sonably simple examples, he constructs a new approach which is a 
superset of the methods proposed by/Gazdax 1979/and/Karttunen 
and Peters 1979/. This rococo approach to naturM lazlguage presup- 
positions has been argued against on methodological and empirical 
lines in/Mercer 1987/. 
By reappraising the insightful counterexamples to Gazdar's theory 
given in/Soaznes 1982/, it is noticed that the semantic representation 
of'if.., then' sentences that contain a sententiM adverb in either the 
424 
antecedent or consequent clause plays an important role in determin- 
ing the presuppositions of the sentence. The inferential theory for 
natural language presuppositions described in \]Mercer 1987, 1988\] 
gives a simlde and straightforward explanation for the presupposi- 
tions\] nature of these sentences. 

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