It is a common truth that the simplest and most obvious questions are often particularly difficult to answer. For instance, when meeting new people I get confronted with the very reasonable but disturbing question What are you doing for work?. I normally answer that I do research in linguistics and hope that this will stop all further inquiries. Sometimes, this does not work and the questioner continues asking what is it that I am investigating. That is where the real trouble starts. The most correct answer would probably be that I am studying meaning, more precisely, the meaning of expressions of natural languages like English. But what is this meaning? There are so many facets to it, so many ways to look at meaning that it is hardly possible to give a satisfying and compact answer to this question. Already the very vague description just given raises a lot of questions. Is it the meaning of words I am considering or the meaning of sentences, for words seem to mean different things in different sentences? Maybe also the level of sentences is not abstract enough. Even for people that have never consciously thought about meaning before it is obvious that sentences mean different things under different circumstances. A sentence like This is my husband may be meant purely to tell the addressee which of the persons in a room is the husband of the speaker. But uttered in a bar to some fellow making you pretty uneasy, you may actually intend to communicate Leave me alone. Or, when you utter the sentence pointing to your dog, you certainly do not mean it to be true in a strict sense. You probably just want to express that you have (in some respects) the kind of relationship with your dog that married women normally have with their husband. Given that the meaning of a sentence depends on its actual use, do we, therefore, rather have to consider the meaning of a concrete occurrence of a sentence? But then we would not be able to account for those aspects of meaning common to all uses of a word or a sentence.

Such considerations have lead to a fundamental distinction in linguistics between the meaning of an expression by itself and the meaning that an expression can obtain through interaction with the context in which it is used. With Grice (1989) one distinguishes two subtypes of meaning. There is, first, semantic meaning - as Grice puts it: what is said. This is the meaning carried by the words themselves. But there is also pragmatic meaning, meaning based on rules governing the use of a particular expression with its semantic meaning. Both semantic and pragmatic meaning together are taken to constitute the meaning of an expression. Semantic meaning is commonly described - at least until the early 80-ties - using truth conditions. Theories for pragmatic meaning are less uniform, but it is very popular to describe this part of meaning using theories of rational behavior such as decision theory and game theory.

However, the picture is still not as clear as these lines might suggest. For one thing, there is still an on-going debate on where exactly the line between semantics and pragmatics has to be drawn. For instance, dynamic semantics, that was developed in the 80-ties, shifts some issues traditionally belonging to pragmatics back into semantics. Furthermore, for many concrete observations on the meaning of natural language expressions it is still unclear whether they should be explained as semantic or pragmatic phenomena. In this dissertation we will discuss three such observations on the interpretation of English sentences for which the question how to account for them, in particular, whether they are effects of semantic or pragmatic meaning, is still conceived as open. For all of them we will develop a theory taking a very specific standpoint with respect to the semantics-pragmatics distinction. Although some of the general ideas underlying these theories are not new, the work presented here differs from other approaches that follow similar lines in the grade of elaboration of these ideas.

The first observation we want to account for is the Free choice inference of disjunctive modal sentences. It has often been observed that sentences like (1) allow the hearer to conclude that both taking a pear and taking an apple are permissible options.

(1) You may take an apple or a pear.

Standard semantic theories have problems in accounting for this observation. We will develop the idea that free choice inferences are actually pragmatic inferences. More particularly, we will account for them as conversational implicatures. One of the major criticisms Grice's theory of conversational implicatures has to face is that it is not able to make precise predictions. We will therefore first develop a partial formalization of this theory, and then show that this formalization allows us to account for the free choice inferences.

The second phenomenon that we will discuss is the particular way we often enrich what is standardly assumed to be the semantic meaning of answers. For illustration, in a dialogue like (2) Bob's answer is often interpreted as exhausting the predicate in question, hence, as stating not only that John and Mary passed the examination, but also that these are the only people that did.

(2) Ann: Who passed the examination?

Bob: John and Mary.

This reading is called the exhaustive interpretation of answers. In Chapter 3 of this dissertation a formal description of this phenomenon is developed that respects its non-standard logical properties and also accounts for dependencies on the form of the answer given and the contextual relevance of the answer. We will argue that the exhaustive interpretation of English answers is part of the pragmatic meaning of answers, more particularly, a conversational implicature. We will support this claim by proving that a simplified version of the description of exhaustive interpretation provided can be derived from the formalization of conversational implicatures introduced in Chapter 2.

Finally, we will discuss the meaning of English conditional sentences. The aspect of the meaning of these constructions that interests us here are primarily their temporal properties. More particularly, we want to explain the apparent discrepancies between the form of English conditional sentences - especially the tense morphology occurring in them - and the temporal interpretation they obtain. For instance, in so-called subjunctive conditionals like (3) the antecedent is marked with the simple past. However, the antecedent cannot be interpreted as referring to the past.

(3) If you asked him, Peter would help you.

We will develop an approach that derives these temporal properties compositionally from the meaning of the parts of the construction. Thus, in contrast to the first two topics, in this case we will make semantics responsible for the observations under debate.

But before we start to consider the temporal properties of English conditional sentences, we will first, in Chapter 5, discuss the meaning of these sentences on a more abstract level that ignores time. The reason is that there are some open questions concerning the meaning of in particular counterfactual conditionals that have to be answered before we can properly account for the temporal properties of conditionals. After this has been done we will, in Chapter 6, extend the timeless framework developed in Chapter 5 with (i) the introduction of a more complex logical form for conditionals with formal expressions for the English tenses, the perfect, and modals will, would, may, and might, and (ii) the addition of time to the model with respect to which the logical form is interpreted. We will provide a compositional semantics for this logical form that correctly accounts for the temporal properties of conditionals under discussion.

Besides their relevance for the semantics-pragmatics debate, there is another way in which the three topics discussed in this book are connected. In all three cases the interpretation of sentences will be described using minimal models. Let us be a bit more explicit on what we mean with the use of minimal models. Assume that you have defined a function I that assigns interpretations to sentences ψ of some formal language L. More precisely, the function I is proposed to map elements of L on subsets of some domain M, which is a class of models for L-sentences. Then we can strengthen the interpretation function I by defining a new interpretation function I* that maps a sentence ψ of L to some subset of I(ψ). This subset can be defined, for instance, as the set of minimal elements of I(ψ) with respect to some order ≤ on M: I*(ψ) = Min(≤, I(ψ)). In this case we say that we have defined the interpretation function using minimal models.

In the second and the third chapter we will use minimal models primary to formalize pragmatic reasoning. More particularly, we will use them to make parts of Grice's theory of conversational implicatures concrete. In this context the function I will refer to semantic meaning of a sentence and I* to a strengthening of semantic meaning with pragmatic information. In the second part of the book, the Chapters 4, 5, and 6, minimal models will be used to model the semantic meaning of conditional sentences. As standard in the literature, we will claim that a conditional with antecedent A and consequent C is true in a world w, if the consequent holds on those worlds making the antecedent true that are most similar to w. These most similar worlds are defined as the minimal models with respect to some order comparing similarity. Also in this context, the function I refers to an (abstract version) of semantic meaning. But I* is a semantic interpretation function as well. The operation * is proposed to be part of the meaning of the conditional connective. A central contribution of the present work on conditionals lies in the way it specifies the similarity relation - and thereby the operation *. We claim that laws, in particular causal laws, play an important role for similarity.