View source for Compact event notation

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>

: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 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{gray}. P(e)</math>

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.
# The event variable <math>e</math> being bound is given by the following '''superscript'''.
# 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 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.

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"
|+ Compact event notation
|-
! Compact notation !! Expanded notation
|-
| <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{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{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{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==

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

:<math>\exists e.\ \tau(e) \subseteq{} \text{t}_0 \land{} \text{AGENT}(e)(\text{w}) = \text{jı} \land{} \text{ruaq}_{\text{w}}(\lambda w.\ \exists e'.\ \tau(e') \subseteq{} \text{t} \land{} \text{AGENT}(e')(w) = \text{jı} \land{} \text{tao}_{w}(\text{a})(e'))(e)\ |\ \text{t} < \text{t}_0\ |\ \text{abstract}(\text{a})</math>

Using compact notation, it becomes a bit less daunting:

:<math>\exists \mathop{\text{ruaq}}\limits_{\subseteq{}\text{t}_0}{}^{e}_{\text{w}}\left(\text{jı}; \lambda w.\ \exists \mathop{\text{tao}}\limits_{\subseteq{}\text{t}}{}^{e'}_{w}\left(\text{jı}; \text{a}\right)\right)\ |\ \text{t} < \text{t}_0\ |\ \text{abstract}(\text{a})</math>