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Figure 2 illustrates classes for each relationship along with its typical logical interpretation.
Conjunctive and disjunctive are relationships that have customary symbols used in a similar way in the propositional logic.
Each one is assigned a distinctive grammatical feature.
We use an abbreviation (Conj, Disj, Adver, Ill) to label the corresponding transformations that describe the relationship of the grammatical structures to the semantics involved. |
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There are two senses for the term conjunctive as applied to a relationship.
We often use the adjective conjunctive to refer to the use of and, one of the connectives to join clauses, words or phrases.
Hence, as a grammatical feature we also mean the combining or conjoining of multiple clauses with an AND( ) relationship.
This relationship is part of the analysis of all of the conjoining relationships in some use (even sometimes with the disjunctive).
In interpreting the conjunctive relationship we note that the logical connective is symmetric.
Symmetric means that if the connective relates p to q it must also relate q to p in the same way.
Any lack of symmetry between the paraphrastic versions of the clauses, i.e., the underlying propositions, would indicate that order is important — that the clause sequence is conveying some additional albeit dependent relationship such as time (tense).
The disjunctive and the adversative relationships are also symmetric, but the illative is not symmetric.
Another feature used in the interpretation of relationships is transitive.
Transitive means that if the connective relates p to q and also q to r it must also relate p to r in the same way.
Except for the adversative relationship, the other three basic relationships in figure 2 are transitive.
Here again absence of transitivity in the use of the corresponding connectives will indicate the presence of some additional relationship. |
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The logical AND( ), i.e., the conjunctive relation uses the conjunction and.
This relation means that asserting this combination of p with q is the same as asserting p and q separately.
If either p or q is false or both of them are false, then the combination is also false.
AND( ) is both symmetric and transitive. |
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The logical OR( ), i.e., the disjunctive relationship uses the conjunction or.
This relation means that asserting this combination of p with q is the same as asserting either p or q separately.
Only if both p and q are false is the combination also false.
OR( ) is both symmetric and transitive.
These functors grammaticalize as [+Disjunctive]. |
| 'But' is a fence over which few venture. | — German Proverb* | |
| There is no simple logical connective for the adversative meaning in the conjunction but.
The proposal first introduced in chapter seven was to use a couple of concepts that we may define in more primitive terms.
We defined the predicate PROBABLE( ) to mean that the probability of a particular proposition holding is at least 0.5.
We also introduced in chapter five the predicate EXCLUSIVE( ).
This was a logical relation that may hold between sets or situations asserted by p and q,
and meaning that the sets corresponding to p and q have no members in common.
With situations we say that they are different and do not co-occur.
The adversative relation will usually hold, for example, when we express p as the negative corresponding to q as the positive, or vice versa.
The adversative relationship is both symmetric and transitive since its components all have these features.
These functors grammaticalize as [+Adversative]. |
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The illative relationship, i.e., the logical consequence is expressed by the conjunction therefore.
This means that asserting the combination of p with q is the same as asserting the dependence of q on p.
Only if p is true and at the same time q is false, would the combination be false. As with the adversative, the predicate PROBABLE( ) is also involved.
The predicate CONTAIN( ) is a logical relation that may hold between sets or situations asserted by p and q.
Use of this predicate means that the members of the second set are all members also of the first, or that the first situation does not occur unless the second one does also.
The illative relationship is not symmetric, but it is transitive.
These functors grammaticalize as [+Illative]. |
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One finds words and phrases associated grammatically using mostly the same connectives as used to conjoin clauses.
In this chapter we concentrate on the conjoining of clauses and delay detailed coverage of the conjoining of words and phrases until the next chapter.
Still, because English often favors grammatical conjoining of words and phrases rather than their clausal counterparts, we use in this chapter some examples that more properly belong in chapter ten. |
| We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'. | |
| — Arthur Eddington, early 20th century, in A. L. Mackay (ed.), Dictionary of Scientific Quotations* | |
| The four basic conjunctions of compound sentences have very clear and definite meanings when interpreted as logical mathematical relationships.
Eddington is probably thinking about and in the mathematical sense.
Yet there is also a literary sense.
In English literature compound sentences may carry some additional baggage.
This motivates another principle to guide the paraphrastic analysis — the principle of secondary meanings. |
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The author will usually modify the conjoining of independent clauses or else combine the clauses so as to imply the presence of other logical attributes.
For example, a clause may be positive or negative as it relates to another clause.
In use a simple disjunction is usually either an inclusive disjunction or an exclusive disjunction.
Often it is the author’s choice of connective that indicates the presence or absence of additional attributes.
Examples will illustrate compounding where various adverbial relations find expression, e.g., conditional, causative, temporal.
These adverbial relations are sequentive, i.e., it is the sequential order of the clauses that determines the interpretation.
Some are dependent, e.g., whenever there is a time-sequentive relation, the relation is also positive and inclusive.
We use the term alternative to describe a feature that often occurs with disjunction — an implicit understanding of opposites.
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