Disjunction in an Entailment Relation: Experimental Evidence for a Modification to Hurford’s Constraint, and the Consequences for a Logical Framework

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Disjunction in an Entailment Relation:

Experimental Evidence for a Modification to Hurford’s

Constraint, and the Consequences for a Logical Framework

Koen Keune 10003527

Bachelor thesis Credits: 18 EC

Bachelor Opleiding Kunstmatige Intelligentie University of Amsterdam Faculty of Science Science Park 904 1098 XH Amsterdam Supervisor dr. F. Roelofsen June 27th, 2013

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1 Introduction

Disjunction is represented differently in various logical frameworks. In classical logic, a disjunction is true if either one of its disjuncts are true, which has been the standard treatment of disjunction in linquistics. However, recent work in lin-quistics has argued for a refinement of the classical approach, allowing a better representation of disjunction in certain contexts. This paper discusses two of those refinements: inquisitive semantics, and alternative semantics. In inquisitive se-mantics, disjunctive sentences are treated as those which introduce alternatives, whereas alternative semantics allow a more flexible representation of disjunction.

I have tested the validity of certain predictions of two theories about disjunctive sentences in a particular context, namely, disjunctive sentences where the disjuncts stand in an entailment relation. An example of such a sentence: ‘John was born in Paris or France’. In this sentence John was born in Paris entails that he is born in France (entailment in this context can be seen as ‘is included in’). Hurford’s Constraint predicts that these type of sentences are infelicitous (Chierchia et al., 2009, p. 2). Singh (2008) and Chierchia et al. (2009) propose two different the-ories that predicts when a disjunctive sentence falls into Hurford’s Constraint. It

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was investigated whether only sentences where the second disjunct entails the first disjunct can obviate Hurford’s Constraint, as was predicted by Singh. Furthermore, it was investigated whether only scalar sentences can obviate Hurford’s Constraint, assumed by Chierchia et al., and predicted for most cases by Singh. Finally, the variation between scalar sentences was examined, and compared with the results of van Tiel et al. (2013)

This paper gives experimental evidence that sentences where the first disjunct entails the second disjunct can obviate Hurford’s Constraint, and that non-scalar sentences can obviate Hurford’s Constraint. Two surveys were conducted to arrive at the results. The participants had to judge for themselves whether a sentence was infelicitous or not. A sentence was classified as felicitous if the average judge-ment was in a 95% confidence interval that it was judged felicitous above 50%. The results showed that three sentences where the first disjunct entails the second were judged felicitous, and that two non-scalar sentences were judged felicitous. Contrary to some of the predictions made by Singh, and Chierchia et al.. From the significant amount of disjsunctive sentences in an entailment relation, and the inability of the theories to predict when such sentences should be represented is concluded that alternative semantics, for now, has an clear advantage over inquisi-tive semantics representing those sentences.

The purpose of this paper was to discover how people judge sentences in Hur-ford’s constraint, and what the consequences are for the theories of Singh (2008) and Chierchia et al. (2009), and generally for alternative and inquisitive semantics. New evidence to a modification of Hurford’s Constraint was found by asking for the judgement of people about those sentences with a yes or no question. This ev-idence is included in the discussion how inquisitive, and alternative semantics are able to represent those sentences.

The paper is organized as follows. The logical frameworks are explained in more detail in section 2.1, and the theories about Hurford’s Constraint are ex-plained in more detail in section 2.2. The methods, results and conclusions for each survey, and the corpus research are discussed in subsections in section 3. Fi-nally, section 4 discusses and concludes all the results, and are followed by the consequences of the results for the logical frameworks.

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2 Literature review

This literature review explains how disjunctive sentences in an entailment relation are represented on two levels. Firstly, it explains how some logical frameworks represent such sentences. Secondly, it explains the theories of Chierchia et al. (2009), and Singh (2008) which are about disjunction in an entailment relation.

2.1 Disjunction in a logical frameworks

There are different approaches to capture the meaning of sentences. The difference comes from a difference in view on what is important to capture. The difference in view expresses itself with a different representation for disjunction among oth-ers. How disjunctive sentences in an entailment relation should be represented is important for a logical framework because that may have consequences on the de-sign of the respective logical framework. The dede-sign of the logical frameworks, alternative semantics and inquisitive semantics, are a refinement of the classical approach. Therefore, how disjunction is represented in the classical approach is explained first, this will be followed by discussing the difference between alterna-tive and inquisialterna-tive semantics in their representation of disjunction. After that, two theories about the representation of disjunctive sentences in an entailment relation are discussed.

2.1.1 Classical approach

The representation of disjunction in the classical approach works as a join operator. A disjunctive sentence in classical logic ‘joins’ the sets of possible worlds that their propositions specify. S, the possible worlds for the disjunctive sentence ‘A or B’ are all of the possible worlds of A plus the possible worlds of B, to illustrate,

w1 w2 w3 w4 or w1 w2 w3 w4 becomes w1 w2 w3 w4 Figure 1 2.1.2 Alternative semantics

A disadvantage of the classical approach regarding disjunction is that it inter-prets certain sentences different from how people would interpret such sentences.

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Alonso-Ovalle (2009) shows that it is possible in alternative semantics to represent some of those sentences in agreement with the interpretation of people, namely, the possibility to represent counterfactuals with disjunctive antecedents correctly. An example of such a sentence is,

(1) If we had had good weather this summer or the sun had grown cold, we would have had a bumper crop. (Alonso-Ovalle, 2009, p. 208)

Sentence (1) is represented incorrectly with a standard minimal change semantics in classical logic. In a standard minimal change semantics the consequent is true in the world(s) in which the antecedent is true that are as close as possible to the actual world (Alonso-Ovalle, 2009, p. 208). In sentence (1) the antecedent ‘we had good weather this summer’ leads to a bumper crop. What the other antecedent is does not matter in classical logic because there is already one antecedent that always leads to the consequent, and consequently ignores incorrectly the other antecedent. In other words, ‘the sun had grown cold’ will be ignored.

Alonso-Ovalle (2009) circumvents this problem in alternative semantics by giving disjunction in counterfactuals a different meaning. Disjunction should be-have as an union operator whenever there are counterfactuals. Now both an-tecedents in the counterfactual must lead to the consequence. The new meaning is possible because according to (Alonso-Ovalle, 2009, p. 211) disjunctions intro-duce a set of propositional alternatives. The alternatives are the result of a Hamblin-style alternative semantics. In this semantics, expressions can be expressed in such a way that if there is some operation over multiple expressions that results in a new expression, then the new expression can still access those expressions. In this framework or is represented as a set of propositions and or operates over the deno-tation of A and B for the disjunctive sentence A or B. A or B denotes the union of Aand B, and now both A and B can be accessed from the set of propositions of the whole disjunction. This new meaning of disjunction can be represented as follows:

w1 w2 w3 w4 or w1 w2 w3 w4 becomes w1 w2 w3 w4 Figure 2

The ability to access A and B is essential for the representation of disjunctive counterfactuals and makes other representations for disjunctive sentences possible,

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such as disjunctive sentences in an entailment relation. A disjunctive sentence in an entailment relation can be represented similarly as disjunctive antecedents in a counterfactual. The disjunct that entails the other disjunct can be represented such that it can be accessed from the whole proposition, the following picture illustrates this, w1 w2 w3 w4 or w1 w2 w3 w4 becomes w1 w2 w3 w4 Figure 3 2.1.3 Inquisitive semantics

The representation of disjunction in inquisitive semantics is different from alter-native semantics. The representation of disjunction showed in figure 2 and 3 is not possible in inquisitive semantics, this comes from the fact that inquisitive se-mantics has a different focus on capturing the meaning of sentences. Inquisitive semantics focusses on capturing the inquisitive content, in addition to the informa-tive content. The inquisiinforma-tiveness is an essential aspect of inquisiinforma-tive semantics, and generalizes the classical approach for meaning (Ciardelli et al., 2013).

The meaning of a sentence in this framework can be seen as a function that maps the previous discourse context to a new discourse context. The discourse that is focussed on is one in which participants exchange information by raising and resolving issues. To make this possible, a sentence has an information exchange potential, this consists of the potential to provide information and the potential to raise issues. The information established so far is modelled as a certain set of possible worlds . The actual world is located somewhere in this set of possible worlds. A sentence provides information by making the current set of possible worlds smaller than what they were before the sentence. An issue that a sentence raises comes from a request to locate the actual world more precisely inside the set of possible worlds. An issue is represented as a non-empty set I that locates the actual world with sufficient precision. If I contains an enhancement s, and t ⊂ s is a further enhancement of s, then t must also be in I. As a result, I is downward closed. I also forms a cover of the current set of possible worlds because every world in the established set of possible worlds is possible with the available information so far (Ciardelli et al., 2013, p. 4).

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Figure 4 shows an example of how the disjunctive sentence, ‘John or Mary will go to the party’, can be represented in inquisitive semantics. The first boolean tells if John will go to the party and the second boolean tells if Mary will go to the party. The informative content of the sentence is the same in the classical logic approach, but the inquisitive content tells that it is either the case that the set of all worlds where John is going to the party are true or it is the case that the set of all worlds where Mary is going to the party are true.

11 10 01 00 or 11 10 01 00 becomes 11 10 01 00

Figure 4: representation in inquisitive semantics of ‘John or Mary will go to the party’

An advantage of inquisitive semantics over alternative semantics is that it is broader in scope, since it captures inquisitive content in addition to informative content, this is particularly relevant for questions. Questions especially have in-quisitive content because, normally, when someone is asking a question a certain answer is sought-after. Therefore, inquisitiveness could explain questions better and is an advantage over a logical framework who cannot explain questions in such a way.

Another advantage of inquisitive semantics over alternative semantics is that inquisitive semantics is downward enclosed. A more solid logical foundation is possible as a result of this. So form the ordering of the informative and inquisitive content a Heyting algebra (Ciardelli et al., 2013, p. 4). The fact that inquisitive semantics is downward enclosed makes it impossible to represent a subset of the the whole set of possible worlds like in figure 2. Every subset of the total set of possible worlds is a further enhancement of the information established so far, and thus every subset of the total set of possible worlds is also a proper set of possible world(s). In this setting, it does not make much sense to single out one of those subsets (like in figure 3). The representation of disjunction is therefore different from alternative semantics, and it makes the representation of disjunctive sentences in an entailment relation different from alternative semantics. Inquisitive semantics can only represent a disjunctive sentence in an entailment relation if the actual meaning of such a sentence would be such that the disjuncts do not entail each other, for example, consider the following sentence:

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Sentence (2) could be represented in inquisitive semantics if the actual meaning would be:

(3) John was born (in France but not in Paris) or (in Paris).

The disjuncts in sentence 3 do not entail each other any more, and the sentence can now be represented in inquisitive semantics. An advantage of this represen-tation is that it gives an explanation why a sentence is felicitous or not because if it can represent such a sentence then there is must be some kind of strengthened meaning such that the entailment is gone. For this, inquisitive semantics needs a theory that predicts consistently a strengthened meaning for such sentences. The following section is about two theories that make such predictions.

2.2 Disjunction in an entailment relation

Disjunctive sentences in an entailment relation can seem infelicitous in certain cases. Such sentences can be felicitous if the ‘strengthened meaning’ of those sen-tences is such that there is no entailment between the disjuncts of the disjunctive sentences any more. According to the neo-Gricean approach to scalar implicatures, the strengthened meaning of a sentence can be calculated on the basis of the lit-eral meaning of the sentence and its scalar alternatives. The strengthened meaning of disjunctive sentences in an entailment relation can give an explanation for the felicity of the sentence. For instance, the sentence ‘A or B or both’ can be seen as infelicitous because ‘both’ entails ‘A or B’. On the other hand ‘A or B’ could implicate ‘A or B but not both’, and then there is no entailment any more and the sentence should not be infelicitous.

There are two types of disjunctive sentences in an entailment relation: scalar and non-scalar sentences. The difference between the two is that for scalar sen-tences it is often assumed that there alternatives are members of the same lexical scale whom are ordered in terms of their informativeness (van Tiel et al., 2013, p. 1), whereas non-scalar sentences cannot be ordered on the same lexical scale. An example of an scalar sentence:

(4) The food is cheap or free.

Cheap and free are on the same scale, with free being more informative than cheap. On the contrary, the following sentence is non-scalar:

(5) John was born in Paris or in France.

The sentence is non-scalar because the alternatives cannot be on the same scale, because if it were then the alternatives would be on the following scale: {John is

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from Paris, John is from Lyon, John is from Nancy, ... , John is from Paris}. The strengthened meaning of John is from Paris would then mean that ‘he is not born from Paris, Lyon, etc’ and this would lead to a contradiction.

When a sentence can be strengthened does not mean that it should be strength-ened, this depends whether people infer a strengthened meaning. van Tiel et al. (2013) found experimental evidence showing that there is a difference whether peo-ple strengthen a sentence between scalar items. It was observed, for instance, that people derived a scalar inference more often between cheap and free than between content and happy (van Tiel et al., 2013, p. 8). It was found that the distinctness between the words was a significant factor for the variation between scalar items.

The strengthened meaning can be calculated with an syntactic operator which takes two arguments, a set of alternatives ALT and a sentence S (Chierchia et al., 2009, p. 1). Singh (2008) and Chierchia et al. (2009) both made predictions when and how such an operator should work regarding disjunctive sentences in an en-tailment relation. They both propose a modification to Hurford’s Constraint, this is explained firstly, secondly the paper of Chierchia et al. is explained in more detail, and lastly the paper of Singh is explained in more detail.

2.2.1 Hurford’s Constraint

Hurford (1974) proposed the generalization that disjunctive sentences in an entail-ment relation are infelicitous. This generalization is now generally referred to as Hurfords Constraint (Chierchia et al., 2009, p. 2). Formally stated, a sentence that contains a disjunctive phrase of the form S or T is infelicitous if S entails T or T entails S. Gazdar (1979) noticed that Hurfords Constraint appears to be obviated in some cases. These cases have an ambiguity and this ambiguity comes from scalar items. Gazdar proposed that a sentence is not infelicitous if a scalar implicature of the first disjunct in conjunction with the first disjunct contradicts the second dis-junct. With this generalization, one could say that whether Hurfords Constraint should be obviated involves some kind of implicature cancellation mechanism, such a mechanism should find out if an implicature of the first disjunct can lead to a contradiction with the second disjunct. The implicature cancellation mecha-nism can only look at sentences as a whole, and is in line with the neo-Gricean approach (Chierchia et al., 2009, p. 3).

2.2.2 Chierchia et al. (2009)

Chierchia et al. (2009) claims that Hurford’s Constraint is correct as originally stated and does not involve an implicature cancellation mechanism. The appar-ent violations of Hurford’s Constraint could be explained with an

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computing operator on scalar implicatures in an embedded position. The implicature-computing operator is part of the grammatical system, and therefore allows inser-tion in an embedded posiinser-tion. The implicature-computing operator is called an exhaustivity operator, represented as exh. The operator exh applies to a sentence S (the prejacent) and a set of alternatives, and returns the conjunction of S and the negation of all the alternatives that are not entailed by S. Sentences do not violate Hurford’s Constraint any more if the prejacent can be ‘strengthened’ such that the conjunction of S, and the negation of some scalar alternatives that are non-weaker than S can break the entailment relation (Chierchia et al., 2009, p. 10). The fol-lowing sentence can now satisfy Hurford’s Constraint (instead of violating it): (6) Peter either solved both the first and the second problem or all of the problems

The sentence can be strengthened with exh at the first disjunct, which leads to the following structure: exh(Peter solved the first problem and the second problem) or he solved all of the problems, which is equivalent to:

(7) Either Peter solved the first problem and the second problem and no other problem, or he solved all the problems

All of the possible alternatives are omitted, but have the structure ‘Peter solved X’, where X denotes one of the problems or a plurality made up of some of the problems. The sentence now satisfies Hurford’s Constraint because the second disjunct does not entail the first disjunct any more. Contrary to Gazdar’s gen-eralization because the strengthened meaning can only be accomplished with an embedded implicature, which is not possible with Gazdar’s generalization.

Chierchia et al. (2009, p. 6) also claims that the operator exh can be embedded within the first disjunct such that the correct reading arises.

2.2.3 Singh (2008)

Singh (2008) agrees with Chierchia et al. for the need of the generation of impli-catures in embedded positions for sentences with disjuncts in an entailing relation. Singh (2008) provides evidence that the exhaustivity operator is only available for earlier disjuncts, in line with Chierchia et al. (2009) (there is not made an argument for this assumption in the paper of Chierchia et al.). The order of the disjuncts in these sentences matter. The disjunctive sentence X or Y will first be checked if it violates Hurford’s Constraint, before Y will be strengthened by exhaustification. In other words, Hurford’s Constraint should be checked incrementally at each dis-junct to the right before it can be strengthened by implicature. The strengthened disjunct should create an inconsistency with the other disjunct.

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Another point that is made in Singh (2008) is that X or Y should not brake the entailment, but should create an inconsistency to obviate Hurford’s Constraint. The Hamblin denotation is used to be able to create alternatives for sentences that are not scalar. The following sentence would be infelicitous

(8) John was born in Russia or in Asia.

The sentence is infelicitous because Russia and Asia are not entirely incon-sistent with each other and there is no relevant implicature for Russia that would create an inconsistency with Asia. According to Singh (2008) the strengthened meaning of a sentence X or Y can be checked with an dialogue, this holds scalar and non-scalar disjuncts. The dialogue can be done by asking Is it the case that X?, if the response can be No, only Y then that would be evidence that X could mean X and not Y and Hurford’s Constraint can be obviated. If the response cannot be No, only Y, then Hurford’s Constraint is violated. Crucially is that the Hamblin notation of the question has to include the conjunctive alternative (Singh, 2008, p. 11).

To summarize, Singh (2008) argues like Chierchia et al. (2009) for an embed-ded implicature-computing operator, but stresses that it can only be placed at the first disjunct, and it should be checked incrementally. Furthermore, the strength-ened meaning is can be checked with an dialogue, and disjuncts in a disjunctive sentence that are consistent with each other should also be added to Hurford’s Constraint.

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3 Testing the two theories

Certain aspects of the theories of Singh (2008) and Chierchia et al. (2009) were tested with two surveys and a corpus research. The first survey tested quantita-tively whether the order of disjuncts in a disjunctive sentence in an entailment rela-tion matter, as is argued by Singh (2008). The second survey tested quantitatively whether Hurford Constraint can only be obviated on scalar implicatures. Finally, a corpus analysis was performed to find support for the order of scalar items investi-gated by van Tiel et al. (2013), and also tested in the second questionnaire.

3.1 First survey, the order of the disjuncts

The prediction that the exhaustivity operator is only available for earlier disjuncts (Singh, 2008) was tested with a questionnaire. The prediction would be correct if the sentences where the first disjunct entails the second disjunct were judged sig-nificantly lower for the same sentence where the disjuncts are reversed. Concretely, the prediction is that the following could be judged felicitous:

(9) She was mad or angry.

The exhaustivity operator can strengthen the first disjunct such that the meaning the first disjunct becomes: mad but not angry. As a result the strengthened sentence is not in Hurford’s Constraint any more. Contrary, the following sentence should not be judged felicitous:

(10) She was angry or mad.

The entailment or consistency cannot be broken by strengthening angry and should fall therefore in Hurford Constraint.

Method

There were 25 participants of which 17 of them were employees of a secondary school, the rest were acquaintances. The questionnaire was in Dutch, however there should not be a significant difference between languages because Hurford’s Constraint makes a prediction about the underlying structure of sentences, and this structure is not lost in Dutch. The questionnaires were filled in independently of one another.

In the questionnaire, the participants had to judge whether various disjunctive sentences in an entailment relation are infelicitous (95% certainty that more than 50% of the people judge them felicitous). The participants had to answer yes if they could see themselves use the respective sentence in a certain context, and

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had to answer no if they did not think it was the case because the sentence is a weird sentence. A sentence is classified as infelicitous if the answer regarding that sentence is no, this was not asked directly because directly asking about the felicity might have been unclear for some participants.

The questionnaire consisted of 20 sentences of which 2 of them were control sentences to test if they understood the question correctly. All the sentences had a structure of:

(11) A or B, with A → B or B → A.

There were 9 sentences where the first disjunct entailed the second disjunct and 9 sentences where the second disjunct entailed the first disjunct. Almost every sentence was formulated differently with for every sentence a similar sentence but with the order of the disjuncts reversed. An example of this is (see appendix A for the questionnaire):

(12) Jelle and Kristen or Jelle or Kirsten went on vacation.

And for the same type of sentence but with the disjuncts reversed: (13) John or Marlies, or John and Marlies went to the party.

Results and discussion

Six out of a total of 444 answers had both or none of the boxes filled in, these an-swers were been given a weight of an half. Table 1 shows the results (see appendix C figure 5 for the results for each sentence). The results in table 1 indicates that there is not a significant difference in the judgement of people in the order of the disjuncts in an entailment relation, the averages between the sentences are almost the same. The results are not conclusive because there was only 1 sentence, where the first disjunct entails the second, judged felicitous. The sentence that was judged felicitous (translated in English): ‘the train leaves every quarter of an hour or every half hour’. A possible explanation that this sentence is judged felicitous is that is a numerical expression, and numerical expressions could implicate a stronger reading more often. It could be possible that there is only a difference in the order of the disjuncts of the sentences that are judged felicitous, except for numerical expressions. A wider range of types of sentences in a survey could result in more conclusive results.

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Table 1:The judgement of different disjunctive sentences in an entailment relation. Leg-end: mean = average of sentences that were judged felicitous. NF = number of sentences in 95% confidence interval that were judged felicitous above 50%, NI = number of sentences in 95% confidence interval that were judged infelicitous above 50%, N = total number of sentences

Type of sentence mean (%) NF NI N All sentences 29 1 12 18 First disjunct entails the second 29 1 7 9 Second disjunct entails the first 29 0 5 9

3.2 Second survey, scalar and non-scalar sentences

The second survey investigated whether only scalar sentences can obviate Hur-ford’s Constraint. The exhaustivity operator in the paper of (Chierchia et al., 2009) can only obviate sentences from Hurford Constraint if they are scalar items. Singh (2008) predicts that the operator could also be applied on non-scalar sentences that can be strengthened with the Hamblin denotation. A second survey was conducted to examine whether only scalar sentences can obviate Hurford’s Constraint. The non-scalar sentences began with the stronger disjunct. The main problem of the first experiment was that there was only one sentence that was judged felicitous with the stronger disjunct first. Beginning with the stronger disjunct could give more conclusive results than experiment 1. Additionally, the difference between the judged felicity of scalar sentences were compared with the difference between derived scalar inferences of the same scalar items, as was observed in van Tiel et al. (2013).

Method

There were 20 participants, all of them were acquaintances. The questionnaire was in Dutch, and the questionnaires were filled in by the participants independently of one another.

In the questionnaire, the participants had to judge whether disjunctive sen-tences in an entailment relation were infelicitous, yes if so and no if not. The ques-tionnaire was similar to the first quesques-tionnaire, only they were now asked directly if a sentence was infelicitous, it was assumed that this would make the questionnaire clearer.

The questionnaire consisted of 40 different disjunctive sentences in an entail-ment relation. The difference between scalar and non-scalar sentences was tested by asking about the infelicity of 20 scalar sentences and 20 non-scalar sentences. The 20 scalar sentences consisted of scalar items of the experiment of van Tiel et al.

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(2013) to test whether the same variation could be found. The second disjunct en-tailed the first disjunct for the scalar sentences, to be able to compare it with the results of van Tiel et al. Van Tiel et al. found a variation between the percentage of participants who derived a stronger scalar item between various scalar items. A high percentage means that people read a strengthened for the particular item, and could result in the conclusion that the sentence is infelicitous because the entailing relation is gone in the strengthening meaning.

The first disjunct entailed the second disjunct for the non-scalar sentences, to test the results of experiment 1. The results of experiment indicate that the order of the disjuncts do not matter, thus a fair comparison between the scalar and non-scalar sentences should be possible.

An example of a scalar sentence in the questionnaire (see appendix B for the questionnaire):

(14) The shirt was dark or black. Results and discussion

One non-scalar sentence was excluded from the results because the sentence was on closer inspection not a non-scalar sentence. Two out of a total of 800 answers were missing. Table 2 shows the difference in judgement between scalar and non-scalar sentences (see appendix C figure 6 for the results for each sentences). Table 3 shows the judgement of the scalar sentences compared with the results for the same scalar items of van Tiel et al., it shows only the scalar items of the sentences that were judged felicitous and infelicitous because they gave the most clear results. Table 2: The judgement of scalar and non-scalar disjunctive sentences in an entailment relation. Legend: mean = average of sentences that were judged felicitous (1 - percentage of the judgements). NF = number of sentences in 95% confidence interval that they were judged felicitous above 50%, NI = number of sentences in 95% confidence interval that they were judged infelicitous above 50%, N = total number of sentences

Type of sentence mean (%) NF NI N All sentences 47 17 12 39 Scalar sentence 48 2 7 19 Non-scalar sentence 45 2 6 20

The results in table 2 show that scalar and non-scalar items in a disjunctive sentence in an entailment relation can both be judged felicitous (2 scalar sentences were judged felicitous, and 2 non-scalar sentences), and is in contrast with the predictions of Singh and Chierchia et al.. Chierchia et al. made only predictions

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about scalar sentences that can obviate Hurford’s Constraint and become felici-tous. Singh predicted that non-scalar sentences could be felicitous only if they can be strengthened with the exhaustivity operator at the first disjunct, and the second disjunct should be strengthened for the non-scalar sentences that were in the ques-tionnaire. The sentences cannot be strengthened according to Singh because the second disjunct should be strengthened.

The judgement of the non-scalar sentences is comparable with the judgement of the scalar sentences, despite a different position of the entailing disjuncts (48% for scalar and 45% for non-scalar). The sentences in the second survey were overall judged felicitous at a higher rate than the first survey, this may have been caused for the most by a difference in questioning the judgement. The participants in the second survey were asked directly if a sentence was infelicitous, instead of asking indirectly whether a sentence was felicitous. Nevertheless, the comparable judgements between a different order of the disjuncts are in line with the results of the first survey, and the two non-scalar sentences that were judged felicitous give more conclusive evidence that sentences where the first disjunct entails the second can be felicitous.

The two non-scalar sentences that were judged felicitous were (with the orig-inal sentence in Dutch after each sentence, because there is possibly a difference between languages):

(15) a. There is tomorrow a party or something. Originally: Er is morgen een feest of iets. b. As long as it is a necklace or jewelry.

Originally: Zolang het maar een ketting of een sieraad is.

The sentences above cannot be strengthened with an exhaustivity operator in the traditional sense because ‘party or something’, and ‘necklace or jewelry’ are not on the same scale. A possible explanation that sentence (15) a., was judged felicitous is that ‘or something’ could implicate ‘or something else’. Sentence (15) b., could have been judged felicitous because people possibly do not think that a necklace is jewelry, instead they might think of diamonds as instances of jewelry but not a necklace.

It should be noted that these sentences may have been judged felicitous in En-glish. The scalar inferences that are inferred can be different for the same word between languages, for example ‘some’ in Dutch can be instantiated as ‘sommige’ or ‘enkele’, and have a different rate of upper-bounding inferences between them (Banga et al., 2009).

The results in table 3 show inconclusive results. Generally, the sentences cor-responded roughly with the percentage of participants who mentioned a stronger

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Table 3: List of the judgement of scales compared to the results of Legend: mean = average of sentences that were judged felicitous. SI = percentage of participants who mentioned a stronger scalar item in the modified cloze task (Exp. 3, lenient analysis), (van Tiel et al., 2013, p. 8). +N = in a neutral condition. -N = in a non-neutral condition.

Scale Scale in Dutch mean (%) SI(+N) SI(-N) hfew,nonei hweinig,geeni 80 75 54 hcheap,freei hgoedkoop,gratisi 75 100 93 hwarm,hoti hwarm,heeti 30 75 64 hintelligent,brillianti hslim,briljanti 30 8 7

hugly,hideousi hlelijk,afschuwelijki 30 4 18 hlike,lovei hleuk,houdt ervani 25 50 25 hstart,finishi hstart,finishi 25 21 21 hpalatable,deliciousi hsmakelijk,heerlijki 20 58 61

scalar item. An example of a sentence that was judged as was expected by the results of van Tiel et al., was the sentence with the scalar items cheap and free. A possible explanation of the difference is that some words in Dutch can implicate a stronger or weaker reading than in English. A possible explanation why certain sentences were judged felicitous is that ‘none’ and ‘free’ are at the end of the scale. Similarly, the sentences that were judged infelicitous are not at the end of a scale (except start or finish), and there meaning is similar to each other. A more extensive research was done to possibly arrive at more conclusive results.

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3.3 Corpus research

An corpus research was performed to find more conclusive results for the diversity in upper-bounding inferences of scalar expression found by van Tiel et al. (2013). A problem of the results in the second survey was that the results were not sig-nificant enough, and it was in a different language. The advantage that a corpus research has, is that it can circumvent the language problem, and the possibility to find more conclusive results. The central question that was examined was: can the same diversity be found of inferred upper-bounding scalar inferences in a (large) corpus?

Method

The corpus research was done with a program in python that searched for particular disjunctive sentences in the Open American National Corpus (2014). The OANC consists of 14.6 million words, from which 3.2 are spoken words. The program counted every disjunctive sentence that consisted of one of the 44 scalar item pairs of van Tiel et al. A sentence was counted if the program detected a structure of a sentence as specified by a regular expression. The structure had to be in a sen-tence and must begin with the weaker scalar item, followed by or, followed by the stronger scalar item, and in between those three words possibly text. Every found structure was manually checked to see whether the disjuncts stood in an entailing relation. An example of a structure that the program found for the words ‘few’ and ‘none’: ‘few inflections or none at all...’. The number of occurrences for each pair was divided by the total occurrences of each scalar item to be able to compare the results with the results found by van Tiel et al.

Results and discussion

The results of the corpus research can be seen in table 4. The results show the scalar item pairs that were found of the 44 pairs in total, searched in a corpus of 14.6 million words.

Table 4 show that disjunctive sentences with the same scalar items of van Tiel et al., are really rare, only ‘some or all’ occurred more often than three times. The sentences are too rare in the OANC to compare properly with the results of van Tiel et al., only five out of 44 pairs occurred in the corpus. Multiple words occured less than 1000 and even less than 100 times. Therefore, it may have been possible that the lack of results are the result of an unfortunate corpus choice, or are the result of a corpus that is not large enough.

Most of the structures of the five sentences that occurred in the corpus had a structure of: ‘scalar word 1 or scalar word 2’, without words in between them.

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Table 4: All the sentences that occurred at least one time in the OANC. Legend: NW = total number of occurrences of the weaker scalar item, NS = total number of occurrences of the stronger scalar item, N = total number of occurrences in a disjunctive sentence, with the weaker item first.

Scalar item pair NW NS N hsome,alli 23508 38659 20 hdifficult,impossiblei 1938 600 3

hsometimes,alwaysi 2865 5578 2 hfew,nonei 6046 1466 2 hgood,excellenti 13974 861 1

This fact makes it possible to search directly in large corpora, and was used to test whether a larger and different corpus could result in more results. The sentences were searched in the online search bars of the British National Corpus (about 100 million words, Burnard, 2000), and in the Google Ngram Corpus (over 500 billion words, Michel et al., 2011). Certain sentences that were not found in the OANC were also not found in the other coprora, some sentences that were also not found in the other corpora were: ‘hard or unsolvable’, ‘allowed or obligatory’, and ‘un-settling or horrific’.

I conclude from this that corpus research is not an effective tool if the frequency for various disjunctive sentences in an entailment relation is needed because they are too uncommon.

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4 General discussion and conclusion

Investigating whether various disjunctive sentences in an entailment relation are infelicitous or felicitous has never been done by directly asking the judgement of people. This paper showed the results of two questionnaires to test the predictions of the felicity of those sentences made by Singh (2008), and by Chierchia et al. (2009). The prediction that those sentences cannot be felicitous if the first disjunct entails the second disjunct was tested (predicted by Singh), and the prediction that non-scalar cannot obviate Hurford’s Constraint (predicted for most instances by Singh, and assumed by Chierchia et al.)

The results in table 1, and 2 give evidence that sentences where the first disjunct entails the second disjunct can also be judged felicitous (3 of those sentences were judged felicitous). People overall do not seem to make a difference between the order. There was however a difference in the judgement overall between the first and second survey. There was a difference in the way the judgement was asked in the second survey, and this may have been an important reason for the difference. The first survey had a lower average judgement, and only one sentence was judged felicitous. In the first survey, the participants had to answer ‘yes’ if they could see themself use the sentence in a particular context, and some may have answered ‘no’ because they never use some of those words, but did not necessarily think the sentence was weird.

The results in table 3 give evidence that non-scalar sentences can be judged felicitous (2 of those sentences were judged felicitous). Additionally, even though scalar and non-scalar are two types who seem to be really different the average judgement between the two was surprisingly similar. An explanation could be that they both had there reasons to be judged sentences infelicitous. Some scalar sentences could have been judged infelicitous because the scalar items were near each other on their scale, and stating such a sentence could be interpreted as stating the same thing twice. Whereas the non-scalar sentences could have been judged more infelicitous because of the entailing relation between the two disjuncts that seem weird, the difference in the order of the disjuncts could also have played a role in this.

Another survey could be conducted to find an explanation for the factors that played a role in people’s judgement. Participants could explain briefly for each sentence why they thought it was infelicitous or not. This will also give more insight for the variation between people in judging such sentences.

Finally, it was examined whether the diversity between scalar items on differ-ent scales found by van Tiel et al. (2013) could be reproduced in a differdiffer-ent setting, this was done by looking at the judgement from the scalar sentences from a second survey. These sentences contained scalar items that were compared with the

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per-centage of people that derived a scalar inference for the pair. This could support the hypothesis that sentences are judged felicitous if the disjuncts are strengthened. The results, however, gave inconclusive results (see table 3).

The hypothesis was further investigated with a corpus research, but only gave marginal results (see table 4), and made a proper comparison impossible. The marginal results indicate, along with similar results for larger corpora, that a sig-nificant amount (39 of the 44 sentences in the OANC) are too rare in the corpora existing today to say to what extend they are infelicitous. The conclusion that the lack of results show that those sentences are infelicitous cannot be made because this in contrast what the results of van Tiel et al. and what table 3 indicates. An explanation for this discrepancy may be found by comparing corpus results with the results of an extensive survey over those results.

4.1 Consequences for a logical framework

The eventual goal was to get an better understanding of disjunctive sentence in an entailment relation, so that a logical framework could represent those sentences properly. There were two logical frameworks discussed in the literature review, al-ternative semantics and inquisitive semantics. Alal-ternative semantics can be seen as a more flexible framework because it can access the expression that each disjunct represents. In inquisitive semantics this is only possible if a expression is not cov-ered in a more general expression. At first glance, this is exactly how disjunctive sentences in an entailment relation seems to be, however an explanation why such a sentence could be felicitous is that the meaning of those sentences is such that there is no entailment between the disjuncts. The theories of Singh, and Chierchia et al. predicted an exhaustivity operator that can strengthen those sentences in such a way.

The results showed that there are certain sentences that were judged felicitous which were not predicted by the theories of Singh, and Chierchia et al. From this can be concluded that people assign some kind of meaning to those sentences, and should be represented in a logical framework that represents informative content. Therefore, those theories needs to be modified to be able to explain the results. Until a theorie can predict when, and how all types of those disjunctive sentences should be represented the more flexible logical framework alternative semantics seems better suited.

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References

Open american national corpus, 2014. URL: http://http://www.anc. org/data/oanc.

Luis Alonso-Ovalle. Counterfactuals, correlatives, and disjunction. Linguistics and Philosophy, 32(2):207–244, 2009.

Arina Banga, Ingeborg Heutinck, Sanne M Berends, and Petra Hendriks. Some implicatures reveal semantic differences. Linguistics in the Netherlands, 26:1, 2009.

Lou Burnard. The british national corpus users reference guide. October 2000. URL: http://www.natcorp.ox.ac.uk.

Gennaro Chierchia, Danny Fox, and Benjamin Spector. Hurfords constraint and the theory of scalar implicatures. Presuppositions and implicatures, 60:47–62, 2009.

Ivano Ciardelli, Jeroen Groenendijk, and Floris Roelofsen. Inquisitive semantics: a new notion of meaning. Language and Linguistics Compass, 7(9):459–476, 2013.

Gerald Gazdar. Pragmatics: Implicature, Presupposition and Logical Form. Aca-demic Press, New York, 1979.

James R Hurford. Exclusive or inclusive disjunction. Foundations of Language, pages 409–411, 1974.

Jean-Baptiste Michel, Yuan Kui Shen, Aviva Presser Aiden, Adrian Veres, Matthew K Gray, Joseph P Pickett, Dale Hoiberg, Dan Clancy, Peter Norvig, Jon Orwant, et al. Quantitative analysis of culture using millions of digitized books. science, 331(6014):176–182, 2011. URL: https://books.google.com/ ngrams.

Raj Singh. On the interpretation of disjunction: Asymmetric, incremental, and eager for inconsistency. Linguistics and Philosophy, 31(2):245–260, 2008. Bob van Tiel, Emiel van Miltenburg, Natalia Zevakhina, and Bart Geurts. Scalar

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Appendix A: Questionnaire of Experiment 1

De vragenlijst gaat over een bepaald type zinnen. In de vragenlijst moet u over elke zin apart oordelen of u de zin in een bepaalde context zou kunnen gebruiken, of dat u de zin niet zou gebruiken omdat het een rare zin is.

De klusjesman komt vandaag of morgen. Het gras was nat of doorweekt.

De vuilniswagen haalt de groene of de blauwe, of allebei de containers op. Alle auto’s of sommige auto’s reden te hard.

Robin had een van zijn schoenen of beide schoenen al aan. Jennifer was geboren in Engeland of Londen.

Mariska had beide schoenen of een van haar schoenen al aan getrokken. Arnoud had sommige of alle aanbevolen boeken gelezen.

De postbode komt elke week of elke dag.

Op het speelveld speelden kinderen of de kinderen van de buren buiten. Nu of straks.

Mandel was geboren in Parijs of Frankrijk.

Jelle en Kirsten of Jelle of Kirsten gingen op vakantie. John of Marlies, of John en Marlies gingen naar het feestje. De trein vertrekt elk kwartier of elk half uur.

Fabrice had alle of sommige aanbevolen boeken gelezen. Het gras was doorweekt of nat.

De vuilniswagen haalt allebei de containers op, of de groene of de blauwe. Nikola at alle of enkele pepernoten.

Ze was boos of razend.

Appendix B: Questionnaire of Experiment 2

De vragenlijst gaat over een bepaald type zinnen. In de vragenlijst moet u over elke zin aangeven of het een rare/ongebruikelijke zin is (ja voor raar). Het is niet de bedoeling dat u hierover lang nadenkt.

De opdracht was voldoende of goed gemaakt. Het shirt is donker of zwart.

In de wasmand zitten broeken of kleren. Het eten is goedkoop of gratis.

Onze kat of een kat was buiten.

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De wind is koel of koud.

Het hekje was met rode verf of met verf geschilderd. Deze film is grappig of hilarisch.

De bioloog zag weinig of geen vogels. Het insect is klein of minuscuul. Ze was op vakantie in Rome of Itali.

Er komt dancemuziek of muziek uit die auto. Het schilderij is lelijk of afschuwelijk.

Het Nederlands elftal of een voetbalteam speelt. Eet een appel of eet fruit.

Ze gingen naar het strand of naar het water. Die professor is slim of briljant.

Dinsdag moet ze presenteren of wat zeggen. De voetballer was moe of uitgeput.

Ze zag sommige of alle aanwijzingen. Als het maar een ketting of een sieraad is.

Hij kon niet slapen vanwege de harde muziek of vanwege het harde geluid. De atleet was gestart of gefinisht.

Deze cd is schaars of niet te verkrijgen. Het was vandaag warm of heet.

Er is morgen sneeuw of neerslag. Er is morgen een feest of iets.

Neem een paracetemol of een medicijn. Je kunt ernaar toe via een snelweg of een weg. De puzzel is moeilijk of onoplosbaar.

De prinses vindt het leuk of houdt ervan om te dansen. Het huiswerk mag of moet gemaakt worden.

De koffiebonen komen van Brazili of Zuid-Amerika. Ze houdt van breien of van handwerken.

De jongen heeft een hekel aan broccoli of verafschuwt broccoli. De buren hebben een hond of een huisdier.

De maaltijd was smakelijk of heerlijk. De boom was groot of enorm.

Ze las een roman of een boek.

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Disjunction in an Entailment Relation: Experimental Evidence for a Modification to Hurford’s Constraint, and the Consequences for a Logical Framework