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Semantics: Difference between revisions
Mention the special syntax for presuppositions in lambda expressions
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Note that this <math>\text{defined only if}</math> clause can appear anywhere within an expression, not just at the top level. One example where it ''needs'' to be embedded in a sub-expression is in {{Derani| |Gaq tú deo ké pao âq}}. This becomes: <math>\forall a : \text{deo}(a).\ \exists e.\ \tau(e) \subseteq \text{t}\ \land\ \text{gaq}(a, [\text{P}(a)\text{, defined only if }\text{pao}(\text{P}(a), a)])(e)</math>. Moving the <math>\text{defined only if}</math> clause to the top level wouldn't work, because it uses the variable <math>a</math>, which is only available inside the scope of the <math>\forall</math> function. | Note that this <math>\text{defined only if}</math> clause can appear anywhere within an expression, not just at the top level. One example where it ''needs'' to be embedded in a sub-expression is in {{Derani| |Gaq tú deo ké pao âq}}. This becomes: <math>\forall a : \text{deo}(a).\ \exists e.\ \tau(e) \subseteq \text{t}\ \land\ \text{gaq}(a, [\text{P}(a)\text{, defined only if }\text{pao}(\text{P}(a), a)])(e)</math>. Moving the <math>\text{defined only if}</math> clause to the top level wouldn't work, because it uses the variable <math>a</math>, which is only available inside the scope of the <math>\forall</math> function. | ||
In lambda expressions, you might also come across the syntax <math>\lambda a : \text{naokua}(a).\ \text{ti}(\text{t}\mathrm{\acute{i}}\text{qra}, a)</math>, where <math>\lambda</math> is imagined to be a quantifier restricted by <math>\text{naokua}(a)</math>. This is the same thing as writing <math>\lambda a .\ (\text{ti}(\text{t}\mathrm{\acute{i}}\text{qra}, a)\text{, defined only if naokua}(a))</math>. | |||
== Propositions == | == Propositions == | ||