Arguments

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In semantic analysis every proposition contains one predicate and a varying number of referring expressions (noun phrases) called arguments.The predicate may be a verb, an adjective, a preposition, or a noun phrase.
The arguments that accompany the predicate have different semantic functions, or roles, in the proposition. What roles they have depends partly on the nature of the predicate and partly on their own meanings.

Syntactic and Semantic Analysis

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The description of a sentence is a syntactic analysis. The description of a proposition is a semantic analysis. A syntactic analysis is an account of the lexemes and function words in a sentence, describing how these combine into phrases, and showing the functions that these lexemes and phrases have in the sentence. There are somewhat different ways of doing syntactic analysis, but generally these sentence functions are recognized: subject, predicate, object, complement and adverbial.
Note that every lexeme and function word is assigned to one of the syntactic functions, subject, predicate, etc., and these functions are listed in the order they have in the sentence.

The semantic analysis deals with meaning, the proposition expressed in the sentence, not necessarily with all the function words in the sentence. In semantic analysis we first separate Inflection from Proposition.

When Inflection—including Tense—is separated from Proposition, we see that the forms of the verb be (am, is, are, was, were) have no meaning. They are clearly part of the syntactic structure of sentences but not of the semantic structure.

Inflection

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An English sentence has certain kinds of modification that, together, we call inflection. Inflection includes tense (the distinction between present walk and past walked, for instance); aspect (are walking, have walked), and modality (may walk, could walk, should walk, among other possibilities). Tense, aspect and modality can be combined, as in were walking, should be walking, would have walked.

A Proposition is Something Abstract but Meaningful

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A proposition is something abstract but meaningful. It can be expressed in different sentences and in parts of sentences, perhaps with differences of focus but always with the same basic meaning.
And, as you recall, any sentence can be expressed in different utterances, produced by different people at different times and in different places.

A proposition can be Expressed in Different Sentences

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2a Helen put on a sweater.
2b Helen put a sweater on.

These are different English sentences, but they convey the same message—they express the same proposition.

3a Richard wrote the report.
3b Richard is the one who wrote the report.
3c The report was written by Richard.
3d The report is what Richard wrote.

We may say that these four sentences also express a single proposition but they differ in focus: 3b and 3c give a special emphasis to Richard, 3d emphasizes the report, and 3a has no particular focus. In the approach taken here, a proposition does not have a focus; a sentence may add a focus and may add the focus in different places and in different ways. The four sentences about Richard embody the same proposition. A proposition, then, can be realized as several different sentences.

Sentence and Proposition

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A traditional way of defining a sentence is ‘something that expresses a complete thought.’ This definition is a rather strange way of explaining since it assumes that we know what a complete thought is and with this knowledge can determine whether something is or is not a sentence. But surely the procedure must be the reverse. Sentences are more knowable than thoughts. In spite of individual differences speakers of a language generally agree about what is or is not a sentence in their language. Who can say what a complete thought is? Compare these language expressions:

1a We walk in the park.
1b our walk in the park
1c for us to walk in the park

We call the first a complete sentence, and in writing we begin with a capital letter and end with a period. We say the other two are not complete sentences. But all three expressions have the same semantic content, the same relation to an action or possible action performed in a certain place by two or more people, one of whom is the speaker or writer. The difference is grammatical. The first expression asserts something, makes a statement. The other two expressions can be parts of statements, as for instance:

We enjoyed our walk in the park.
It’s not too late for us to walk in the park.

but they do not make assertions by themselves. The formal differences among these three expressions—we, our and us, for example—are a matter of grammar, not semantics.

The semantic content shared by the three expressions is a proposition. A simple statement like We walk in the park expresses asingle proposition, something presented as a fact and therefore subject to verification; generally speaking, one can find out if the proposition is true or false. We don’t walk in the park is the negation of this proposition, and Do we walk in the park? is a question about it.

Truth-conditional Semantics

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Truth-conditional semantics is based on the notion that the core meaning of any sentence (any statement) is its truth conditions. Any speaker of the language knows these conditions. If a sentence is true (or false), what other sentences, expressing partly the same,
partly different conditions, can be judged by this sentence? If a given sentence is true, does this make another sentence also true, or does it falsify the other sentence, or is there no truth relation? Matters of truth and logic are of more importance in truth-conditional semantics than meanings of lexemes per se.
We are not yet finished with the dimensions of meaning. Often we derive more meaning from what we hear or read than what is actually in the message. Perhaps this is due to an intuition we have or to the fact that the speaker or writer infers something—hints at some further meaning. In semantics we are not interested in intuitions or hints but we are interested in the instances when the language of the message implicates some additional meaning that accounts for our inference.

Sentence Meaning

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We communicate with utterances, and each utterance is an instance of a sentence. But how can we explain what ‘sentence meaning’ is?
Two points are obvious. First, the meaning of a sentence derives from the meanings of its constituent lexemes and from the grammatical meanings it contains. So if you know all the lexical and grammatical meanings expressed in a sentence, you know the meaning of the sentence, and vice versa. Second, at least if the sentence is a statement, if you know the meaning of the sentence, you know what conditions are necessary in the world for that sentence to be true.

Albert Thompson opened the first flour mill in Waterton.

You don’t know whether this sentence is true or not, but you know that if it is true, there must exist (at some time) a person named Albert Thompson and a place called Waterton (presuppositions), that Albert Thompson opened a flour mill, and that there was no flour mill in Waterton before Albert Thompson opened his mill (entailments). You know that if this sentence is true, the sentence Albert Thompson did not open the first flour mill in Waterton is false (a contradiction).

Lexical Ambiguity

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When homonyms can occur in the same position in utterances, the result is lexical ambiguity, as in, for example, “I was on my way to the bank.” Of course, the ambiguity is not likely to be sustained in a longer discourse. A following utterance, for example, is likely to carry information about depositing or withdrawing money, on the one hand, or, on the other hand, fishing or boating. Quite often homonyms belong to different lexical categories and therefore do not give rise to ambiguity. For instance, seen is a form of the verb see while scene is an unrelated noun; feet is a plural noun with concrete reference, feat is a singular noun, rather abstract in nature; and so on.
Ambiguity occurs also because a longer linguistic form has a literal sense and a figurative sense.
Skeleton in the closet can mean ‘an unfortunate event that is kept a family secret.’ With this meaning skeleton in the closet is a single lexeme; with its ‘literal’ meaning it is a phrase composed of several lexemes.

Homonymy and Polisemy

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A lexeme is a conjunction of form and meaning. The form is fairly easy to determine: in writing it is a sequence of letters, in speech a sequence of phonemes. But meaning is more difficult to determine.
In homonyms, such as bank ‘a financial institution’ and bank ‘the edge of a stream,’ pronunciation and spelling are identical but meanings are unrelated. In other pairs, numerous in English, such as steak and stake, pronunciation is identical but spelling is different, reflecting the fact that the words were once different in their phonological form. English also has pairs of homographs, two words that have different pronunciations but the same spelling; for example, bow, rhyming with go and referring to an instrument for shooting arrows, and bow, rhyming with cow and indicating a bending of the body as a form of respectful greeting.

Lexicographers and semanticists sometimes have to decide whether a form with a wide range of meanings is an instance of polysemy or of homonymy. A polysemous lexeme has several(apparently) related meanings. The noun head, for instance, seems to have related meanings when we speak of the head of a person, the head of a company, head of a table or bed, a head of lettuce or cabbage. If we take the anatomical referent as the basic one, the other meanings can be seen as derived from the basic one, either reflecting the general shape of the human head or, more abstractly, the relation of the head to the rest of the body.

Dictionaries recognize the distinction between polysemy and homonymy by making a polysemous item a single dictionary entry and making homophonous lexemes two or more separate entries. Thus head is one entry and bank is entered twice. Producers of dictionaries often make a decision in this regard on the basis of etymology, which is not necessarily relevant, and in fact separate entries are necessary in some instances when two lexemes have a common origin. The form pupil, for example, has two different senses, ‘part of the eye’ and ‘school child.’ Historically these have a common origin but at present they are semantically unrelated. Similarly, flower and flour were originally ‘the same word,’ and so were the verbs to poach (a way of cooking in water) and to poach (‘to hunt [animals] on another person’s land’), but the meanings are now far apart and all dictionaries treat them as homonyms, with separate listing. The distinction between homonymy and polysemy is not an easy one to make. Two lexemes are either identical in form or not, but relatedness of meaning is not a matter of yes or no; it is a matter of more or less.

Morphemes

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A lexeme may consist of just one meaningful part like these:

arm chair happy guitar lemon shoe

or of more than one meaningful part like these armchair unhappy guitarist lemonade shoehorn The technical term for a minimal meaningful part is morpheme.
Arm, chair, happy, guitar, lemon, shoe and horn are all morphemes; none of them can be divided into something smaller that is meaningful. They are free morphemes because they occur by themselves. The elements un-, -ist and -ade in unhappy, guitarist and lemonade respectively, are also morphemes; they are bound morphemes which are always attached to something else, as in these examples.

Lexical and Grammatical Meanings

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A dog barked.
The above is a meaningful sentence which is composed of smaller meaningful parts. One of the smaller parts is the phrase a dog which refers to a certain animal. We call this phrase a referring expression.
A referring expression is a piece of language that is used AS IF it is linked to something outside language, some living or dead entity or concept or group of entities or concepts. Most of the next chapter is about referring expressions. The entity to which the referring expression is linked is its referent. Another meaningful part is the verb bark, which is also linked to something outside of language, an activity associated, here, with the referring expression a dog. We call this meaningful part a predicate. The use of language generally involves naming or referring to some entity and saying, or predicating, something about that entity. The sentence also has several kinds of grammatical meanings. Every language has a grammatical system and different languages have somewhat different grammatical systems. We can best explain what grammatical meanings are by showing how the sentence A dog barked differs from other sentences that have the same, or a similar, referring expression and the same predicate.
Grammatical meanings, then, are expressed in various ways: the arrangement of words (referring expression before the predicate, for instance), by grammatical affixes like the -s attached to the noun dog and the -ed attached to the verb bark, and by grammatical words, or function words, like the ones illustrated in these sentences: do (in the form did), not, a, some, and the. Now let’s return to dog and bark. Their meanings are not grammatical but lexical, with associations outside language. They are lexemes. A lexeme is a minimal unit that can take part in referring or predicating. All the lexemes of a language constitute the lexicon of the language, and all the lexemes that you know make up your personal lexicon. The term ‘lexeme’ was proposed by Lyons (1977:18–25) to avoid complexities associated with the vague word ‘word.’

(a) go, going, went, gone
(b) put up with, kick the bucket, dog in the manger

How many words are there in group (a)? Four or one? There are four forms and the forms have four different meanings, but they have a shared meaning, which is lexical, and other meanings of a grammatical nature added to the lexical meaning. We say that these four forms constitute one lexeme which, for convenience we designate as go. Group (b) presents a different sort of problem. The expression put up with combines the forms of put and up and with, but its meaning is not the combination of their separate meanings. Therefore put up with, in the sense of ‘endure,’ ‘tolerate,’ is a single lexeme. The same must be true of kick the bucket meaning ‘die’ and dog in the manger when it refers to a person who will not let others share what he has, even though he does not use it himself.