Compact event notation: Difference between revisions

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When following Toaq's [[semantics]] algorithm, a certain pattern shows up often: an existential quantification of an event, combined with its aspect and verb participant information. For example, {{t|Luı heaqdo jí súq máq }} becomes  
When following Toaq's [[semantics]] algorithm to turn Toaq sentences into logical formulas, many simple clauses translate into an existential quantification of an event, combined with its aspect and verb participant information. For example, {{t|Luı heaqdo jí súq máq}} becomes  


:<math>\exists e. \tau(e) < \mathrm{t} \wedge \text{heaqdo}_w(\text{suq},\text{maq})(e) \wedge \text{AGENT}(e)(w) = \text{jı} \color{teal} \wedge P(e)</math>
:<math>\exists e. \tau(e) < \mathrm{t} \wedge \text{heaqdo}_w(\text{suq},\text{maq})(e) \wedge \text{AGENT}(e)(w) = \text{jı}</math>


:There is an event ''e'', whose runtime precedes the implicit tense ''t'', and which is an event of {{t|heaqdo}}-ing {{t|súq máq}} in world ''w'', and whose agent is {{t|jí}}, (and which satisfies ''P''(''e'').)
:There is an event ''e'' of {{t|heaqdo}}-ing {{t|súq máq}} in world ''w'', whose runtime precedes the implicit tense ''t'', and whose agent is {{t|jí}}.


[[Kuna]] supports generating a compact notation for this:
[[Kuna]] supports a compact notation for this in its denotation outputs:


:<math>\exists \mathop{\text{heaqdo}}\limits_{< \mathrm{t}}{}^{e}_{w}\left(\text{jı}; \text{suq}, \text{maq}\right) \color{teal}. P(e)</math>
:<math>\exists \mathop{\text{heaqdo}}\limits_{< \mathrm{t}}{}^{e}_{w}\left(\text{jı}; \text{suq}, \text{maq}\right) \color{gray}. P(e)</math>


It works as follows:
It works as follows:


# When an existential quantifier <math>\exists</math> is followed by a Toaq verb, it asserts the existence of an event of that verb.
# When an existential quantifier <math>\exists</math> is followed by a Toaq verb, it asserts the existence of an event of that verb.
# The event variable <math>e</math> being bound is given by the following superscript.
# The event variable <math>e</math> being bound is given by the following '''superscript'''.
# The world variable <math>w</math> the event is in is given by the following subscript.
# The world variable <math>w</math> in which the event is situated is given by the following '''subscript'''.
# The aspect information is given underneath the verb. If it starts with a relational operator <math>< t</math> it abbreviates <math>\tau(e) < t</math>.
# The aspect information is given '''underneath''' the verb. If it starts with a relational operator <math>< t</math> it abbreviates <math>\tau(e) < t</math>.
# The participants are listed in parentheses. If there is an agent, it's separated from the non-agent participants by a semicolon.
# The participants are listed in '''parentheses'''. If there is an agent, it's separated from the non-agent participants by a '''semicolon'''.
# Optionally, a final dot announces the rest of the formula <math>P(e)</math> in which <math>e</math> is bound.
# Optionally, a final '''dot''' announces the rest of the formula <math>P(e)</math> in which <math>e</math> is bound.


There are some variants of the notation, depending on the presence of an agent, of non-agent participants, and of a subsequent statement <math>P(e)</math>:
There are some variants of the notation, depending on the presence of an agent, of non-agent participants, and of a subsequent statement <math>P(e)</math>:
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! Compact notation !! Expanded notation
! Compact notation !! Expanded notation
|-
|-
| <math>\exists \mathop{\text{hao}}\limits_{< \text{t}}{}^{e}_{w}\left( \text{y}, \text{z}\right)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{hao}_w(\text{y},\text{z})(e) </math>
| <math>\exists \mathop{\text{tıjuı}}\limits_{< \text{t}}{}^{e}_{w}\left( \text{y}, \text{z}\right)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{tıjuı}_w(\text{y},\text{z})(e) </math>
|-
|-
| <math>\exists \mathop{\text{hao}}\limits_{< \text{t}}{}^{e}_{w}\left( \text{y}, \text{z}\right). P(e)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{hao}_w(\text{y},\text{z})(e) \wedge P(e)</math>
| <math>\exists \mathop{\text{tıjuı}}\limits_{< \text{t}}{}^{e}_{w}\left( \text{y}, \text{z}\right). P(e)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{tıjuı}_w(\text{y},\text{z})(e) \wedge P(e)</math>
|-
|-
| <math>\exists \mathop{\text{hao}}\limits_{< \text{t}}{}^{e}_{w}\left(\text{x}; \text{y}, \text{z}\right)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{hao}_w(\text{y},\text{z})(e) \wedge \text{AGENT}(e)(w) = \text{x} </math>
| <math>\exists \mathop{\text{heaqdo}}\limits_{< \text{t}}{}^{e}_{w}\left(\text{x}; \text{y}, \text{z}\right)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{heaqdo}_w(\text{y},\text{z})(e) \wedge \text{AGENT}(e)(w) = \text{x} </math>
|-
|-
| <math>\exists \mathop{\text{hao}}\limits_{< \text{t}}{}^{e}_{w}\left(\text{x}; \text{y}, \text{z}\right). P(e)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{hao}_w(\text{y},\text{z})(e) \wedge \text{AGENT}(e)(w) = \text{x} \wedge P(e)</math>
| <math>\exists \mathop{\text{heaqdo}}\limits_{< \text{t}}{}^{e}_{w}\left(\text{x}; \text{y}, \text{z}\right). P(e)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{heaqdo}_w(\text{y},\text{z})(e) \wedge \text{AGENT}(e)(w) = \text{x} \wedge P(e)</math>
|-
|-
| <math>\exists \mathop{\text{ruqshua}}\limits_{< \text{t}}{}^{e}_{w}</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{ruqshua}_w(e)</math>
| <math>\exists \mathop{\text{ruqshua}}\limits_{< \text{t}}{}^{e}_{w}</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{ruqshua}_w(e)</math>

Latest revision as of 01:45, 21 December 2023

When following Toaq's semantics algorithm to turn Toaq sentences into logical formulas, many simple clauses translate into an existential quantification of an event, combined with its aspect and verb participant information. For example, Luı heaqdo jí súq máq becomes

There is an event e of heaqdo-ing súq máq in world w, whose runtime precedes the implicit tense t, and whose agent is .

Kuna supports a compact notation for this in its denotation outputs:

It works as follows:

  1. When an existential quantifier is followed by a Toaq verb, it asserts the existence of an event of that verb.
  2. The event variable being bound is given by the following superscript.
  3. The world variable in which the event is situated is given by the following subscript.
  4. The aspect information is given underneath the verb. If it starts with a relational operator it abbreviates .
  5. The participants are listed in parentheses. If there is an agent, it's separated from the non-agent participants by a semicolon.
  6. Optionally, a final dot announces the rest of the formula in which is bound.

There are some variants of the notation, depending on the presence of an agent, of non-agent participants, and of a subsequent statement :

Compact event notation
Compact notation Expanded notation


Example

The full denotation of Pu tao jí hóq da (i.e. Ruaq jí ꝡä pu tao jí hóq ka) is:

Using compact notation, it becomes a bit less daunting: