§13.10. Defining new prepositions
The term preposition is used here, a little loosely, to mean anything which we add to the verb to be in order to talk about some relation or other. We have seen many examples already, such as:
To be in - The ball is in the box.
To be part of - The lever is part of the slot machine.
These are defined just the way verbs are. Compare the following:
Suspicion relates various people to one person.
The verb to suspect means the suspicion relation.
The verb to be suspicious of means the suspicion relation.
The result of this is that
Hercule Poirot suspects Colonel Hotchkiss.
Hercule Poirot is suspicious of Colonel Hotchkiss.
are exactly equivalent, and so are these two descriptions:
somebody who suspects Colonel Hotchkiss
somebody suspicious of Colonel Hotchkiss
While most prepositions are short ("in", "part of", "suspicious of"), they're free to be longer if need be ("inordinately far away from"): the limit is 30 words, which should be ample.
We can also define verbs as auxiliaries, like so:
The verb to be able to approach means the approachability relation.
Now we can ask if Poirot "can approach" Hotchkiss, and so on.
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![]() | Back to §13.9. Defining new assertion verbs |
![]() | Onward to §13.11. Indirect relations |
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Suppose we are modeling a complex society seething with interpersonal relations of every kind.
Now we want ways to set and unset all of these relations. (In the interests of thoroughness, we may get a bit far-fetched here. It is not recommended in practice that we make the player guess the verb "traduce".)
Because love is a 1-1 relation, a person cannot love more than one other character at a time. Whenever we set a character to love a new person, that person ceases to love the character loved before. It is a fickle world. One to various relations are a bit more open: we can say someone impresses multiple other characters, and our additions to the list do not override the initial ones.
And because this is a one-to-various relation, we can also make statements which set multiple relations at once, so:
Note that the above unsetting is not equivalent to "now the noun does not impress every person" -- which would be ambiguous in spoken English, as well. Various-to-one relations are similar:
Our options for setting and unsetting symmetrical relations are more limited again:
When we unset the symmetrical relation on one side, it is automatically set or unset on the other. It is not necessary to say "the second noun is married to the noun" or "the second noun is not married to the noun", even though that is the case.
And finally, setting groups:
Notice that when we say "the second noun is not related", we remove that person from the group: they are now in a separate group of their own, while the rest of the group's members remain related to one another. And finally, a long litany of test cases, complete with the relations lists:
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Suppose we are modeling a complex society seething with interpersonal relations of every kind.
Now we want ways to set and unset all of these relations. (In the interests of thoroughness, we may get a bit far-fetched here. It is not recommended in practice that we make the player guess the verb "traduce".)
Because love is a 1-1 relation, a person cannot love more than one other character at a time. Whenever we set a character to love a new person, that person ceases to love the character loved before. It is a fickle world. One to various relations are a bit more open: we can say someone impresses multiple other characters, and our additions to the list do not override the initial ones.
And because this is a one-to-various relation, we can also make statements which set multiple relations at once, so:
Note that the above unsetting is not equivalent to "now the noun does not impress every person" -- which would be ambiguous in spoken English, as well. Various-to-one relations are similar:
Our options for setting and unsetting symmetrical relations are more limited again:
When we unset the symmetrical relation on one side, it is automatically set or unset on the other. It is not necessary to say "the second noun is married to the noun" or "the second noun is not married to the noun", even though that is the case.
And finally, setting groups:
Notice that when we say "the second noun is not related", we remove that person from the group: they are now in a separate group of their own, while the rest of the group's members remain related to one another. And finally, a long litany of test cases, complete with the relations lists:
Suppose we are modeling a complex society seething with interpersonal relations of every kind.
Now we want ways to set and unset all of these relations. (In the interests of thoroughness, we may get a bit far-fetched here. It is not recommended in practice that we make the player guess the verb "traduce".)
Because love is a 1-1 relation, a person cannot love more than one other character at a time. Whenever we set a character to love a new person, that person ceases to love the character loved before. It is a fickle world. One to various relations are a bit more open: we can say someone impresses multiple other characters, and our additions to the list do not override the initial ones.
And because this is a one-to-various relation, we can also make statements which set multiple relations at once, so:
Note that the above unsetting is not equivalent to "now the noun does not impress every person" -- which would be ambiguous in spoken English, as well. Various-to-one relations are similar:
Our options for setting and unsetting symmetrical relations are more limited again:
When we unset the symmetrical relation on one side, it is automatically set or unset on the other. It is not necessary to say "the second noun is married to the noun" or "the second noun is not married to the noun", even though that is the case.
And finally, setting groups:
Notice that when we say "the second noun is not related", we remove that person from the group: they are now in a separate group of their own, while the rest of the group's members remain related to one another. And finally, a long litany of test cases, complete with the relations lists:
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