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Semantics: Difference between revisions
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Say that you have an idea of what the world is like—maybe you have a mental model in your head, or maybe you have a database to look things up in. If your knowledge is complete enough, then that model lets you answer a question, or tell whether what someone said is true, by interpreting their words and then "looking up" the answer. But more often than not, people are working with incomplete knowledge. In this case, if someone tells you something, a model lets you interpret their words and then ''work backwards'' from the meaning to figure out what must be true about the world. | Say that you have an idea of what the world is like—maybe you have a mental model in your head, or maybe you have a database to look things up in. If your knowledge is complete enough, then that model lets you answer a question, or tell whether what someone said is true, by interpreting their words and then "looking up" the answer. But more often than not, people are working with incomplete knowledge. In this case, if someone tells you something, a model lets you interpret their words and then ''work backwards'' from the meaning to figure out what must be true about the world. | ||
A note for the adventurous: There are alternative approaches to semantics that don't involve models, such as [https://plato.stanford.edu/entries/proof-theoretic-semantics/#InfIntAntRea proof-theoretic semantics], in which the meaning of a statement is determined purely by its relationships to other statements in a formal proof system. There have been some attempts to apply this approach to Lojban and Toaq semantics<ref>[https://mostawesomedude.github.io/brismu/ brismu], a sketch of an inferential approach to Lojban semantics</ref><ref>[ | A note for the adventurous: There are alternative approaches to semantics that don't involve models, such as [https://plato.stanford.edu/entries/proof-theoretic-semantics/#InfIntAntRea proof-theoretic semantics], in which the meaning of a statement is determined purely by its relationships to other statements in a formal proof system. There have been some attempts to apply this approach to Lojban and Toaq semantics<ref>[https://mostawesomedude.github.io/brismu/ brismu], a sketch of an inferential approach to Lojban semantics</ref><ref>[[:File:Hoemuı.pdf|Hoemuı]], the beginnings of a sketch of an inferential approach to Toaq semantics (super outdated)</ref>, but when it comes to natural language semantics, the model-based approach described here is far more common. | ||
== Basic notation == | == Basic notation == | ||
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== Worlds == | == Worlds == | ||
Another important concept for any semantic theory to cover is '''modality''': the treatment of words such as {{Derani||she}}, {{Derani||daı}}, {{Derani||ao}}, and {{Derani||dı}}. We use these words to make claims not about the actual state of the world, but about possibilities, obligations, or beliefs. The tried and true | Another important concept for any semantic theory to cover is '''modality''': the treatment of words such as {{Derani||she}}, {{Derani||daı}}, {{Derani||ao}}, and {{Derani||dı}}. We use these words to make claims not about the actual state of the world, but about possibilities, obligations, or beliefs. The tried and true system for reasoning about modality, named after philosopher Saul Kripke, is known as '''Kripke semantics'''. | ||
In Kripke semantics, we imagine that there are a multitude of '''worlds''': one world, <math>\text{w}</math>, represents the real world, while others represent alternate timelines. Then, every verb is extended to take a world argument: for example, <math>\exists e.\ \text{saqsu}_\text{w}(\text{j}\mathrm{\acute{i}})(e)</math> computes whether there is an event of the speaker whispering ''in the real world'', with the world variable being written in a subscript for readability. | In Kripke semantics, we imagine that there are a multitude of '''worlds''': one world, <math>\text{w}</math>, represents the real world, while others represent alternate timelines. Then, every verb is extended to take a world argument: for example, <math>\exists e.\ \text{saqsu}_\text{w}(\text{j}\mathrm{\acute{i}})(e)</math> computes whether there is an event of the speaker whispering ''in the real world'', with the world variable being written in a subscript for readability. | ||