Compact event notation

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, Luı heaqdo jí súq máq … becomes

$\mathrm{\exists }e.\tau (e)<\mathrm{t}\wedge {\text{heaqdo}}_w(\text{suq},\text{maq})(e)\wedge \text{AGENT}(e)(w)=\text{jı}\wedge P(e)$

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

Kuna supports generating a compact notation for this:

$\mathrm{\exists }\text{heaqdo}{\mathrm{\backslash limits}}_{<\mathrm{t}}{}_w^e(\text{jı};\text{suq},\text{maq}).P(e)$

It works as follows:

1. When an existential quantifier $\mathrm{\exists }$ is followed by a Toaq verb, it asserts the existence of an event of that verb.
2. The event variable $e$ being bound is given by the following superscript.
3. The world variable $w$ the event is in is given by the following subscript.
4. The aspect information is given underneath the verb. If it starts with a relational operator $<t$ it abbreviates $\tau (e)<t$.
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 $P(e)$ in which $e$ is bound.

There are essentially four variants of the notation, depending on the presence of an agent and of a subsequent statement $P(e)$:

Compact event notation

Compact notation	Expanded notation
$\mathrm{\exists }\text{hao}{\mathrm{\backslash limits}}_{<\text{t}}{}_w^e(\text{y},\text{z})$	$\mathrm{\exists }e.\tau (e)<\text{t}\wedge {\text{hao}}_w(\text{y},\text{z})(e)$
$\mathrm{\exists }\text{hao}{\mathrm{\backslash limits}}_{<\text{t}}{}_w^e(\text{y},\text{z}).P(e)$	$\mathrm{\exists }e.\tau (e)<\text{t}\wedge {\text{hao}}_w(\text{y},\text{z})(e)\wedge P(e)$
$\mathrm{\exists }\text{hao}{\mathrm{\backslash limits}}_{<\text{t}}{}_w^e(\text{x};\text{y},\text{z})$	$\mathrm{\exists }e.\tau (e)<\text{t}\wedge {\text{hao}}_w(\text{y},\text{z})(e)\wedge \text{AGENT}(e)(w)=\text{x}$
$\mathrm{\exists }\text{hao}{\mathrm{\backslash limits}}_{<\text{t}}{}_w^e(\text{x};\text{y},\text{z}).P(e)$	$\mathrm{\exists }e.\tau (e)<\text{t}\wedge {\text{hao}}_w(\text{y},\text{z})(e)\wedge \text{AGENT}(e)(w)=\text{x}\wedge P(e)$

Example

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

$\mathrm{\exists }e.\tau (e)\subseteq {\text{t}}_0\wedge \text{AGENT}(e)(\text{w})=\text{jı}\wedge {\text{ruaq}}_{\text{w}}(\lambda w.\mathrm{\exists }{e}^{\prime }.\tau (e^{\prime })\subseteq \text{t}\wedge \text{AGENT}(e^{\prime })(w)=\text{jı}\wedge {\text{tao}}_w(\text{a})(e^{\prime }))(e)|\text{t}<{\text{t}}_0|\text{abstract}(\text{a})$

Using compact notation, it becomes a bit less daunting:

$\mathrm{\exists }\text{ruaq}{\mathrm{\backslash limits}}_{\subseteq {\text{t}}_0}{}_{\text{w}}^e(\text{jı};\lambda w.\mathrm{\exists }\text{tao}{\mathrm{\backslash limits}}_{\subseteq \text{t}}{}_w^{e^{\prime }}(\text{jı};\text{a}))|\text{t}<{\text{t}}_0|\text{abstract}(\text{a})$