![[P1] The Sentence](gif/bnf/bnf01.gif)
| The predicate calculus needs arguments to fill out a predicate to make it a proposition of the propositional calculus. We need a term in English syntax to refer to the corresponding expressions in English — comprising both noun clauses and noun phrases — that most easily translate as an argument of the predicate calculus. It may not always be clear which of several ways the analyst should carry out the translation or matching of components between the usually very different languages of English and of logic. We will begin by observing that those particular English sentences that allow the most straightforward matching of their various parts with corresponding components of a single logical proposition are the simple sentences. |
| It might be helpful for some to see the way these simple sentences are represented using the semantic net of MultiNet. The interpretations of some of the following sentences in that system have been placed in Excursus J. Ontologies (classification schemes) for help in reading and understanding conceptual entities of that system are in Excursus I. |
The simplest correspondences.Suppose the central proposition underlying a sentence has a single argument. The English speaker usually expresses such a lone argument in the subject of the sentence. |
| Sentence | Proposition | Argument=Subject | |
|---|---|---|---|
| (1) | The people waited. | WAIT(a) | a = "the people" |
| (2) | John was my friend. | FRIEND(a) | a = "John" |
| (3) | The flowers were beautiful. | BEAUTIFUL(a) | a = "the flowers" |
| It is often possible for the predicate in the main proposition to have two arguments; in this case the first is the subject and the second is usually an object of verb or preposition. |
| Sentence | Proposition | Arg=Subject | Arg=Object | |
|---|---|---|---|---|
| (4) | The boy hit the ball. | HIT(a,b) | a = "the boy" | b = "the ball" |
| (5) | There are books on the table. | ON(a,b) | a = "books" | b = "the table" |
| (6) | She is in my class. | IN(a,b) | a = "she" | b = "my class" |
Less direct correspondences.There are also simple sentences which the analyst cannot relate so easily or directly to any underlying proposition. Sometimes the syntactic structure in the subject position does not correspond directly to the logical subject, as in (1) and (2). There are even cases when the English speaker describes the occurrence of certain natural phenomena in such a way that the argument of the main predicate comes out as a verb. |
| Sentence | Proposition | Argument=Subject | |
|---|---|---|---|
| (1) | There are two exceptions. | EXIST(a) | a = "two exceptions" |
| (2) | It is significant that he came. | SIGNIFICANT(a) | a = "it" a = "that he came" |
| (3) | It snowed very hard. | HAPPEN(a) | a = "a very heavy snow storm" |
| Furthermore, there are numerous other ways to form a sentence for which there is no simple predicate when translated to its most obvious logical form. This is the case with the natural language phenomena of metaphor and idiom. The English speaker uses this figure and device as a matter of course to express certain states and relationships. The idiom in (4) illustrates this situation. It does not seem possible to relate the translation into logic directly to the meanings of the individual parts. |
| Sentence | Proposition | Arg=Subject | Arg=Object | Predicate | |
|---|---|---|---|---|---|
| (4) | He has had trouble with the police. | P(a,b) | a = "he" | b = "police" | P = "have trouble with" |
| What does this mean for the linguist who is trying to build a logical grammar of English? Metaphor is spontaneous and idiom is metaphor that has become conventional. These figures of speech are by nature idiosyncratic. It appears that the logician-linguist has to relate the respective logical and syntactic predicates by individual idiosyncratic transformations. Perhaps it is possible then at least to classify the various spontaneous occurrences of metaphor by the form of the particular transformations required to describe them. This is akin to that of the highly successful tree adjoining grammar (TAG). The TAG approach is to associate a syntactic structure to such lexical items as are idiosyncratic in this way. |
Syntax of a clause.As demonstrated in §7-4 there is a description of the structure of a sentence using the framework of a GT grammar: A sentence consists in one or more independent clauses. In the third and seventh paragraphs of that section the description of this requirement uses phrase structure rules: |
![[P2] The Clause](gif/bnf/bnf02.gif)
![[P7] The Subject & Predicate Arguments](gif/bnf/bnf07.gif)
| The logician would normally translate sentences, as we did for those in the first two paragraphs, into a semasiological structure of the simplest kind, one having the following formal pattern: |
 ( ) |
| In the majority of cases the analyst has been able to match structural components of the logical version to various parts of the semantic representation and these to the syntactic phrases in the sentence. It would follow that the simplest description would give a clause some form parallel to this structure — one consisting in a subject and predicate which correspond to the argument with its logical predicate. The linguist may state this analysis formally as in [P1]: a simple sentence is a interjection or an independent clause; and [P2]: the clause may be composed of one or more clauses, which would eventually consist at least in a subject argument, and a predicate. It may also have an adverbial adjunct. In addition its subject argument may sometimes be marked as the subject, e.g. when its form is that of a personal pronoun. By [P3] the predicate contains an auxiliary phrase, a verb phrase, and possibly various adverbial adjuncts at different places. These elements, which may contain other occurrences of a syntactic argument, will appear in later rules, which we will give when we describe objects and complements. |
![[P3] The Predicate](gif/bnf/bnf03.gif)
Components of an argument.Perhaps the most common way to express an argument (as the subject of a sentence or any objects and certain complements in it) is by means of a noun phrase (NP). |
| Sentence | Subject=Noun Phrase | |
|---|---|---|
| (1) | The boy went shopping. | "the boy" |
| The following sentences will be built on the first sentence by expanding the noun phrase subject. The predicate, which is not under discussion at this point, consists of a common idiom being a verb complemented with a gerund. |
| A noun phrase as argument (subject or other part of the sentence) may possibly have an associated non-restrictive adjective clause (CL) in which the language user may express some additional qualifying characteristic of the argument. |
| Sentence | Noun Phrase | C + CL | |
|---|---|---|---|
| (2) | The curly haired boy, who had $20 to spend, went shopping. | "the curly haired boy" | "who" + "(he) had $20 to spend" |
| The second way to express an argument is with a noun clause (CL) marked with a conjunction (C). |
| Sentence | C + CL | |
|---|---|---|
| (3) | That he had $20 to spend may be significant. | "that" + "he had $20 to spend" |
| It is also possible for there to be a non-restrictive adjective clause associated with the noun clause. |
| Sentence | C + CL | C + CL | |
|---|---|---|---|
| (4) | That he had $20 to spend, which is debatable, may be significant. | "that" + "he had $20 to spend" | "which" + "(this) is debatable" |
| Instead of a noun clause the object of a sentence may be a simple quote of another sentence. |
| Sentence | Sentence1 | Sentence2 | |
|---|---|---|---|
| (5) | "I have $20 to spend," said the boy. | "I have $20 to spend" | "the boy said (this)" |
| The syntax of each of these five possible argument structures is diagrammed in figure 5: |
| We account for the various constituencies on the right of [P15]: |
![[P9] The Argument](gif/bnf/bnf15.gif)
| The structure of a clause grammaticalizes a logical proposition connected to the main proposition of the sentence as an argument, or as perenthetic association with that argument. In [P15] the clause to the left expresses a proposition that is the subject (or object or a certain other complement) argument of the logical predicate, which predicate belongs to the proposition of the main assertion as an argument. |
Ordering PS-rules.Notice that this presentation skips rules [P4] through [P6] and [P8] through [P14] for now, so that this last rule presented has the number [P15]. The intervening rules describe the analysis of the elements of the syntactic predicate, which predicate as we noted parenthetically often contains an argument as an object. The GT linguist tries as much as possible to order the phrase structure rules in a sequence so that the ones that define a given constituent further follow after any rules that introduce that particular constituent. The idea is that a set of ordered rules is more powerful than a set of unordered ones. Note, however, that when there are optional constituencies, as in [P15], the options are unordered. |
| The above diagram shows the relationship between the phrase structure rules of this grammar. (Click on the number to see the rule and hyperlinks to discussion relating to it.) It has been impossible to order the rules strictly. This is due to the recursion that naturally occurs in human language. The arrows in orange indicate where the ordering recurses as in [15], where the argument may take the form of a sentence. Recursion is useful in describing the infinite self-embedding of syntactic structures that manifests itself. |
