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Semantics: Difference between revisions
Make constants non-italic, like the refgram
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Toaq is a loglang, which means that from any sentence, we can unambiguously derive its meaning in logic notation. [[Syntax]] describes how this process works; '''semantics''' describes how to interpret the result. | Toaq is a loglang, which means that from any sentence, we can unambiguously derive its meaning in logic notation. [[Syntax]] describes how this process works; '''semantics''' describes how to interpret the result. | ||
The refgram tells you that {{Derani| |Luı nuo sá tıqra nîe náokua}} translates to <math>\exists x: \text{tıqra} | The refgram tells you that {{Derani| |Luı nuo sá tıqra nîe náokua}} translates to <math>\exists x: \text{tıqra}_\text{w}(x).\ \exists e.\ \text{τ}(e)<\text{t}\land \text{nuo}_\text{w}(x)(e)\land \text{nıe}_\text{w}(e, \text{n}\mathrm{\acute{a}}\text{okua})</math>. The reality is that this isn't "just" logic notation: it's a very specific notation that has been purpose-built for describing natural language semantics, and this article will help you understand the core concepts behind it. | ||
== Models == | == Models == | ||
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== Semantic calculus == | == Semantic calculus == | ||
Now, we're ready to talk about notation. When you see something like <math>\exist x: \text{kato} | Now, we're ready to talk about notation. When you see something like <math>\exist x: \text{kato}_\text{w}(x). \exist e. \text{τ}(e) \subseteq \text{t} \land \text{neo}_\text{w}(x, \text{m}\mathrm{\acute{u}}\text{ao})(e)</math>, what you're looking at are a bunch of things from the domain of the model. A lot of these words (<math>\text{kato}</math>, <math>\text{neo}</math>, <math>\exist</math>, <math>\text{τ}</math>, <math>\land</math>) are '''functions'''; some others (<math>\text{m}\mathrm{\acute{u}}\text{ao}</math>) represent literal "things" from the domain, like physical objects, people, and ideas, which we'll call '''individuals'''. Together, these words form an expression that shows you how to calculate the truth value of a specific sentence (in this case, {{Derani| |Neo sá kato múao}}), given that you have the model. | ||
There's a key difference here: In languages like English and mathematics, you can use words to form statements such as "The sky is blue" and "<math>x + 1 = 2</math>", or you can use them to form smaller expressions, like "the author of this book" and "<math>\left\{1, 2, 3\right\}</math>". But in the semantic notation we're looking at, there are no statements, only expressions, because the point of semantics is to examine the values that things denote, including the values of statements themselves. As such, it doesn't make sense to call this a "logic notation", because on its own, it can't form statements. Instead, we'll call it a '''semantic calculus'''. | There's a key difference here: In languages like English and mathematics, you can use words to form statements such as "The sky is blue" and "<math>x + 1 = 2</math>", or you can use them to form smaller expressions, like "the author of this book" and "<math>\left\{1, 2, 3\right\}</math>". But in the semantic notation we're looking at, there are no statements, only expressions, because the point of semantics is to examine the values that things denote, including the values of statements themselves. As such, it doesn't make sense to call this a "logic notation", because on its own, it can't form statements. Instead, we'll call it a '''semantic calculus'''. | ||