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Compact event notation: Difference between revisions
Compact event notation (view source)
Revision as of 01:45, 21 December 2023
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When following Toaq's [[semantics]] algorithm, | 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} | :<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'' | :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 | [[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{ | :<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 | # 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 | 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>: | ||
{| class="wikitable" | {| class="wikitable" | ||
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! Compact notation !! Expanded notation | ! Compact notation !! Expanded notation | ||
|- | |- | ||
| <math>\exists \mathop{\text{ | | <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{ | | <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{ | | <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{ | | <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}. P(e)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{ruqshua}_w(e) \wedge P(e)</math> | |||
|- | |||
| <math>\exists \mathop{\text{marao}}\limits_{< \text{t}}{}^{e}_{w}(\text{jı};)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{marao}_w(e) \wedge \text{AGENT}(e)(w) = \text{jı}</math> | |||
|- | |||
| <math>\exists \mathop{\text{marao}}\limits_{< \text{t}}{}^{e}_{w}(\text{jı};). P(e)</math> || <math>\exists e. \tau(e) < \text{t} \wedge \text{marao}_w(e) \wedge \text{AGENT}(e)(w) = \text{jı} \wedge P(e)</math> | |||
|} | |} | ||
==Example== | ==Example== | ||