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Semantics: Difference between revisions
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One of the most basic jobs of any semantic theory is to define how verbs work. The traditional approach, used widely throughout mathematics, is to represent {{Derani| |Fa jí náomi}} as <math>\text{fa}(\text{j}\mathrm{\acute{i}}, \text{n}\mathrm{\acute{a}}\text{omi})</math>, where the verb is interpreted as a function (here, <math>\left\langle \text{e} \left\langle \text{e}, \text{t} \right\rangle \right\rangle</math>) receiving the subject and any objects as arguments. But sadly, this approach is unable to account for tense, aspect, or adverbs. | One of the most basic jobs of any semantic theory is to define how verbs work. The traditional approach, used widely throughout mathematics, is to represent {{Derani| |Fa jí náomi}} as <math>\text{fa}(\text{j}\mathrm{\acute{i}}, \text{n}\mathrm{\acute{a}}\text{omi})</math>, where the verb is interpreted as a function (here, <math>\left\langle \text{e} \left\langle \text{e}, \text{t} \right\rangle \right\rangle</math>) receiving the subject and any objects as arguments. But sadly, this approach is unable to account for tense, aspect, or adverbs. | ||
Modern semantics research has settled on a single concept to overcome all of these issues: '''events'''. An event is an extra argument passed to a verb representing the action itself; the instance of that verb "happening". For instance, <math>\text{fa}(\text{j}\mathrm{\acute{i}}, \text{n}\mathrm{\acute{a}}\text{omi})(e) | Modern semantics research has settled on a single concept to overcome all of these issues: '''events'''. An event is an extra argument passed to a verb representing the action itself; the instance of that verb "happening". For instance, <math>\text{fa}(\text{j}\mathrm{\acute{i}}, \text{n}\mathrm{\acute{a}}\text{omi})(e)</math> represents whether <math>e</math> is an event of the speaker going to the sea. Whereas the first two arguments represent the participants in the action (the goer and the destination), ''e'' stands for the thing that connects them: the going, or the journey. Then, a sentence like {{Derani| |Fa jí náomi}} can be understood as claiming that there ''is'' such an event: <math>\exists e.\ \text{fa}(\text{j}\mathrm{\acute{i}}, \text{n}\mathrm{\acute{a}}\text{omi})(e)</math>. This system is credited to philosopher Donald Davidson, giving it the name '''Davidsonian event semantics'''. | ||
This gives us a systematic way to deal with adverbs: to modify the verb, modify the ''event variable introduced by the verb''. This is intended to reflect the intuition that "I slept briefly" has the same meaning as "My sleep was brief". For example, {{Derani| |Nuo jîm jí}} can be interpreted as <math>\exists e.\ \text{nuo}(\text{j}\mathrm{\acute{i}})(e) \land \text{jim}(e) </math>. And prepositions work similarly: for {{Derani| |Lao jí nîe jío}} we would use <math>\exists e.\ \text{lao}(\text{j}\mathrm{\acute{i}})(e) \land \text{nie}(e, \text{j}\mathrm{\acute{i}}\text{o}) </math> — "whether there is some event of me waiting that is inside the building". | This gives us a systematic way to deal with adverbs: to modify the verb, modify the ''event variable introduced by the verb''. This is intended to reflect the intuition that "I slept briefly" has the same meaning as "My sleep was brief". For example, {{Derani| |Nuo jîm jí}} can be interpreted as <math>\exists e.\ \text{nuo}(\text{j}\mathrm{\acute{i}})(e) \land \text{jim}(e)</math>. And prepositions work similarly: for {{Derani| |Lao jí nîe jío}} we would use <math>\exists e.\ \text{lao}(\text{j}\mathrm{\acute{i}})(e) \land \text{nie}(e, \text{j}\mathrm{\acute{i}}\text{o})</math> — "whether there is some event of me waiting that is inside the building". | ||
With events in our toolbox, tense and aspect also fall into place. If we imagine that every event has a temporal footprint (the points in time at which it takes place), then it seems reasonable that there should be a function to access this information. We call this <math>\tau</math>, the '''temporal trace function''' (type <math>\left\langle \text{v}, \text{i} \right\rangle</math>). Aspect is then understood as making a claim about an event's temporal structure, relative to a reference time determined by the tense. For instance, {{Derani||tam}} makes the claim that the event's temporal trace lies fully within the reference time: <math>\tau(e) \subseteq \text{t}</math>. (This one comes up a lot, because {{Derani||tam}} is the default aspect.) And {{Derani||luı}} makes the claim that the event's temporal trace comes before the reference time: <math>\tau(e) < \text{t}</math>. | With events in our toolbox, tense and aspect also fall into place. If we imagine that every event has a temporal footprint (the points in time at which it takes place), then it seems reasonable that there should be a function to access this information. We call this <math>\tau</math>, the '''temporal trace function''' (type <math>\left\langle \text{v}, \text{i} \right\rangle</math>). Aspect is then understood as making a claim about an event's temporal structure, relative to a reference time determined by the tense. For instance, {{Derani||tam}} makes the claim that the event's temporal trace lies fully within the reference time: <math>\tau(e) \subseteq \text{t}</math>. (This one comes up a lot, because {{Derani||tam}} is the default aspect.) And {{Derani||luı}} makes the claim that the event's temporal trace comes before the reference time: <math>\tau(e) < \text{t}</math>. | ||