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A '''frame''' is a class of predicates that all, in a certain sense, have their argument places laid out the same way, giving rise to the same grammatical behavior.
A '''frame''' is a class of verbs that all, in a certain sense, have their argument places laid out the same way, giving rise to the same grammatical behavior.


=== Semantic frames ===
== Semantic frames ==
A '''semantic frame''' is a class of predicates that all have the same amount of argument places, of the same '''types''', in the same order.
A '''semantic frame''' is a class of verbs that all have the same amount of argument places, of the same '''types''', in the same order.


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The '''type''' of an argument place says what kind of thing is allowed to go in there:
The '''type''' of an argument place says what kind of thing is allowed to go in there:
* <code>c</code> ("concrete") means anything goes. Usually concrete arguments like "me" or "cats" or "a house", but also clauses/events if it makes sense.
* <code>c</code> ("concrete") means anything goes. Usually concrete arguments like "me" or "cats" or "a house", but also clauses/events whenever it makes sense in that verb.
** For example, {{t|de}}'s first slot is type <code>c</code>. One can say {{t|dẻ súq}} (You're beautiful) or {{t|dẻ sûaq súq}} (The event of your singing is beautiful).  
** For example, {{t|de}}'s first slot is type <code>c</code>. One can say {{t|dẻ súq}} (You're beautiful) or {{t|dẻ sûaq súq}} (The event of your singing is beautiful).  
* <code>0</code> means a place that must be filled with a ''proposition or event''.
* <code>0</code> means a place that must be filled with a ''proposition or event''.
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Thus, a semantic frame can be identified with its '''type signature''', which is just all the types of the argument places listed in a row — traditionally in parentheses.
Thus, a semantic frame can be identified with its '''type signature''', which is just all the types of the argument places listed in a row — traditionally in parentheses.


For example: {{t|leo}} "tries to" and {{t|juoq}} "should" both take one ''concrete'' argument followed by one ''property'' argument. This is expressed by the type signature <code>(c 1)</code>. These predicates have the same type signature, so they belong to the same semantic frame.
For example: {{t|leo}} ("tries to") and {{t|juoq}} ("should") both take one ''concrete'' argument followed by one ''property'' argument. This is expressed by the type signature <code>(c 1)</code>. These verbs have the same type signature, so they belong to the same semantic frame.


Furthermore, each semantic frame in Toaq has an arbitrary '''representative''' chosen for it, used as a handy way to refer to the frame. For example, the semantic frame of all predicates with type signature <code>(c 1)</code> is called the '''LEO (semantic) frame''', which consists of all the predicates whose argument places are just like {{t|leo}}'s.
Furthermore, each semantic frame in Toaq has an arbitrary '''representative''' chosen for it, used as a handy way to refer to the frame. For example, the semantic frame of all verbs with type signature <code>(c 1)</code> is called the '''LEO (semantic) frame'''. LEO consists of all the verbs whose argument places are just like {{t|leo}}'s.


=== Serial frames ===
We say that “{{t|juoq}} is in the LEO frame” or “{{t|juoq}} is in LEO”. We also often just say that “{{t|juoq}} is <code>(c 1)</code>”.
A '''serial frame''' is a class of predicates that all exhibit the same serialization behavior.
 
=== Table of semantic frames ===
TODO
 
== Serial frames ==
A '''serial frame''' is a class of verbs that all exhibit the same serialization behavior.
 
Again, each such frame is identified by a '''serial signature''' and a representative.
 
But this time, the elements of the signature describe "what happens to this argument slot, when this verb is the first part of a serial verb?" rather than "what can this argument slot be filled with?"
 
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* <code>x</code> or <code>c</code> means that this argument place remains untouched and will still be there in the resulting serial verb.
* <code>0</code> means that this place will be subsumed by all of the right-hand verb's arguments:
** <span style="background:#ddf;padding:4px"><b style="color:red">x</b> wants <b style="color:gray">0</b> to be the case</span> + <span style="background:#ddf;padding:4px"><b style="color:#ba0">x</b> sits on <b style="color:green">x</b></span> = <span style="background:#ddf;padding:4px"><b style="color:red">x</b> wants <b style="color:#ba0">x</b> to sit on <b style="color:green">x</b></span>
* <code>1</code> means that this place will be subsumed by all of the right-hand verb's arguments, '''merging''' with its first one:
** <span style="background:#ddf;padding:4px"><b style="color:red">x</b> tries to satisfy <b style="color:gray">1</b></span> + <span style="background:#ddf;padding:4px"><b style="color:#ba0">x</b> sits on <b style="color:green">x</b></span> = <span style="background:#ddf;padding:4px"><b style="color:red">x</b> tries to sit on <b style="color:green">x</b></span>
* <code>2</code> means that this place will be subsumed by all of the right-hand verb's arguments, '''merging''' with its first two:
** <span style="background:#ddf;padding:4px"><b style="color:red">x</b> all reciprocally satisfy <b style="color:gray">2</b></span> + <span style="background:#ddf;padding:4px"><b style="color:#ba0">x</b> agrees with <b style="color:green">x</b> that <b style="color:teal">0</b> is the case</span> = <span style="background:#ddf;padding:4px"><b style="color:red">x</b> all agree that <b style="color:teal">0</b> is the case</span>
* <code>e</code> means that this place will disappear, '''merging''' with "[[Kind|{{t|baq}}]] ''next-verb''".
** <span style="background:#ddf;padding:4px"><b style="color:red">x</b> takes care of <b style="color:gray">e</b></span> + <span style="background:#ddf;padding:4px"><b style="color:#ba0">x</b> is a cat</span> = <span style="background:#ddf;padding:4px"><b style="color:red">x</b> takes care of cat(s).</span>
** Such a slot is known as an '''exhibitor slot''' (hence <code>e</code>), and the resulting serial is a '''genitival serial'''.
* <code>a</code> means that this '''adjectival''' place will disappear, and the following verb's first place is modified, attributively when appropriate or otherwise predicatively, by this adjective:
** <span style="background:#ddf;padding:4px"><b style="color:red">a</b> is small</span> + <span style="background:#ddf;padding:4px"><b style="color:#ba0">x</b> is a cat</span> = <span style="background:#ddf;padding:4px"><b style="color:#ba0">x</b> is a small cat.</span>
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The signature is again written by writing down all the types in parentheses, like <code>(x x 0)</code> or <code>(x e)</code>.
 
There is '''at most''' one non-<code>x</code> in a serial signature. This is because all the other slot types define ''the'' serialization behavior for the verb, and a verb must have one unambiguous serialization behavior! So while <code>(c 0 0)</code> is a valid semantic frame, there cannot be a <code>(x 0 0)</code> serial behavior, as it wouldn't be clear which of the <code>0</code> slots accepts the right-hand verb arguments.
 
Some verbs cannot participate in serials, and are not part of any serial frame.
 
=== Table of semantic frames ===
TODO
 
== How do they relate? ==
''(This is the author's unofficial theory.)''
 
There is a predictable mapping from semantic frames to serial frames.
 
If the semantic frame has more than one "digit" (<code>0</code>, <code>1</code> or <code>2</code>) in it, then the verb cannot serialize. Example: {{t|she}}.
 
If it has exactly one "digit": the serialization behavior is "subordinating", and the serial frame is obtained by replacing all <code>c</code> with <code>x</code>. Example: {{t|tua}}, {{t|leo}}, {{t|taq}}, {{t|mıujeq}}, {{t|huaq}}, {{t|toı}}.
 
If there are no "digits":
* Semantic frame <code>(c)</code> corresponds to serial frame <code>(a)</code>. Example: {{t|nuı}}, {{t|kue}}(?!).
* Semantic frame <code>(c c)</code> corresponds to serial frame <code>(x e)</code>. Example: {{t|hea}}, {{t|kıaı}}, {{t|tuı}}.
* Otherwise (i.e. <code>(c c c)</code> and beyond, like {{t|kuq}}), the verb cannot serialize.