reference experiencer assertion temporality realis reference determinate definite person set situation state reference attributive assertion temporality reference attachment derivation realis reference determinate definite proper person male individual person individual person communicant speaker individual situation state relation reference property assertion temporality derivation realis reference determinate definite object concrete discrete set object abstract ideal quality property gradable non-measurable situation state relation reference agentive assertion affective temporality reference realis reference determinate definite person male individual object concrete discrete instrumental situation event action reference locality assertion temporality existence locative reference expletive realis reference indeterminate indiscriminate reference indeterminate definite object concrete discrete instrumental set object concrete discrete instrumental individual situation state relation situation descriptor local situation descriptor expletive reference element locality assertion temporality class reference attachment derivation locative realis reference determinate definite person non-communicant female individual person set object concrete discrete instrumental set person communicant speaker individual situation state relation situation descriptor local reference assertion derivation locality existence temporality expletive realis reference indeterminate quantitive cumulative number two object abstract relation set situation state relation situation event situation descriptor local situation descriptor expletive reference proposition property assertion agentive temporality derivation temporality reference realis reference determinate definite object abstract situational proposition realis person non-communicant male individual quality property gradable non-measurable situation state relation situation event happening reference derivation experiencer assertion manner temporality degree realis graduator qualitative object abstract situational event happening individual situation event happening situation descriptor modal manner reference property experiencer assertion derivation temporality derivation temporality affective reference cause realis reference determinate definite person male individual object abstract ideal individual person set quality property total situation event happening situation event action

Section 6-1 SEMANTIC ARGUMENTS

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.

Predicates having one argument.  
The simplest correspondences between the semantics and syntax comprise those where the central proposition underlying the sentence has a single argument. The English speaker usually expresses such a lone argument in the subject of the sentence.
SentencePropositionArgument=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"

[The people waited]

The semantic structure of MultiNet as represented in figure 1 has at least four propositions that might be mentioned. The assertion, which contains a number of relations between the speaker, hearer, communication and content as described earlier in chapter 3, is understood from the order of the elements. The reference of the subject noun, people, is parallel to a common noun in the plural and understood to be a set of individuals. From the article provided we may conclude that it refers also to a constant. The temporality of the verb may be surmised from the past tense form attached. The central predication of the syntax seems to be that the people are going through an experience while other possible entities invoved in this state are neither mentioned nor implied.

[John was my friend]

The structure of the second example in figure 2 simplifies the subject by the use of a proper noun. This noun combines some of the reference function of a determiner making its mathematical coorelate an individual constant. The assertion focuses on the attributive function whereby the role of friend is attributed to the subject. This predicate noun is provided with a possessive modifier expressed in MultiNet with the relation of attachment. The immanent relation of kinship is typical of attachment, but the situational social relations such as friend, teacher, doctor, hero, king, and God, also participate in attachment. This particular adjectival modification derives from a pronoun reference to the person communicating as the speaker. The central predication of the syntax seems to be that John is in this role.

[The flowers were beautiful]

The third example in figure 3 focuses on a property of the subject expressed as a predicate adjective. This adjective derives from an abstract noun. The subject refers to a set of individuals and is provided with a determiner. Here again the sentence has a setting in the past as expressed with the form of the copula.

Predicates having multiple arguments.  
It is often the case that the predicate in the main proposition has two or even more arguments; the first is the subject and the second is usually an object of verb or preposition. Consider the following examples:
SentencePropositionArg=SubjectArg=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"

[The boy hit the ball]

The example in figure 4 is a familiar case of two arguments: a subject and an object of the verb. In this case the subject is semantically an active agent, while the object is a passive participant undergoing the effects of the action expressed in the verb.

[There are books on the table]

In figure 5 there are two objects involved, a set of books and a table. The pre-eminent position in the sentence is taken by what grammarians call an expletive. This particle seems to be closely related to the adverb there usually used to point out a location. Indeed, this sentence does in fact locate the books by reference to the table on which they rest. Logically the books are the subject of the sentence and the prepositional phrase locates them so that the table is the object of the preposition. It is their existence in that place that is being asserted by the use of the expletive. Neither existence nor expletive are used by MultiNet, which minimizes the use of syntactic relations. These relations are both restricted to the specification of objects in space and/or time.

[She is in my class]

The sentence in figure 6 illustrates at least two interpretations of the proposition IN(a,b). The first one involves the literal meaning of class as a set of people related socially to one another. It also takes the prepostion in as referring to a locality. The second interpretation is made at the pre-extensional level of analysis and makes the female individual a member of a set of physical objects. In this case the assertion would be about something being in a set in a logical sense. The possessive case of the personal pronoun has this interpretation as well so that I am also a member of the same set of objects (not diagrammed). To make this interpretation we are required to leave the realm of natural language and enter the world of mathematics.

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 (7) and (8). There are even cases as in (9) 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.
SentencePropositionArgument=Subject
(7)There are two exceptions.EXIST(a) a = "two exceptions"
(8)It is significant that he came.SIGNIFICANT(a) a = "it"
a = "that he came"
(9)It snowed very hard.HAPPEN(a)a = "a very heavy snow storm"

[There are two exceptions]

In figure 7 is another example of the use of the expletive that was described in figure 5. In this case the locality (or temporal) placement of the object is not expressed using a preposition. Existence seems to be the only possible predicate to describe the situation. The possible values of the number modifying the subject by means of the determiner are modelled as pre-extensional elements. This number is the count of members in the set of abstract relations denoted by the noun. This noun is in turn derived from a verb. It denotes the result of an action of leaving something out.

[It is significant that he came]

The structure of a complex sentence is usually lost in MultiNet. Figure 8 shows an example containing a noun clause as subject. MultiNet would probably relate the pronoun to the clause by means of the change of sort from situation to situational. The relation of derivation is not appropriate and the clause is semantically a proposition, this one declarative in nature.

[It snowed very hard]

The example in (9) is difficult for a couple of reasons. First, the manner adverbial telling us about the severity of the snow storm has the form of an adjective. This seems to have enticed MultiNet to call these adverbs qualities. In the domain of situation descriptors MultiNet has a modal related only to the validity of a statement as held by the speaker. Thus it seems to slight this whole branch of adverbial description. The second difficulty is the main reason this example was selected. The severity of the snow storm is adverbial so that the argument of the logical predication is the situation — the happening expressed in the verb. The choice here was to admit that this happening is the reference of the subject and relate it to the situation (verb) by means of a derivation.

Metaphor and idiom.  
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 seems to be an earmark of certain natural language phenomena called 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 (10) illustrates this situation. It hardly seems possible to relate the translation directly to the meanings of the individual parts in a logical way.
SentencePropositionArg=SubjectArg=ObjectPredicate
(10)He has had trouble with the police. P(a,b) a = "he" b = "police" P = "have trouble with"

[He has had trouble with the police]

Sentence (10) introduces a number of new concepts, which are discussed in more detail later.
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.

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