I'm looking for a way to specify the number of times an event happens in a Discourse Representation Structure, basically using first order predicate logic. I have the existential and universal quantifiers available, but I'm looking for a way to say for example that an event or state happens a 100 times, not just always or sometimes. I'm thinking set theory might help, but I'm not sure how. Any tips?
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1Exactly 100 or up to 100? – naslundx Mar 28 '14 at 10:24
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Interesting, never heard of Discourse Representation Theory, is this what you're referring to? tl;dr does this introduce new connectives and/or quantifiers, or can it sufficiently effectively be defined in terms of syntax of classical predicate logic. – Nikolaj-K Mar 28 '14 at 10:32
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Yes DRT is what I'm referring to. It's essentially definable in terms of predicate logic. As for you question naslundx: at least 100. – Omdb Mar 28 '14 at 10:56
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There exist at least two things with the property $P$: $$\exists x\exists y(Px\land Py\land x\ne y).$$
There exist at least three things with the property $P$: $$ \exists x\exists y\exists z(Px\land Py\land Pz\land x\ne y\land x\ne z\land y\ne z). $$ ...
There exist exactly two things with the property P: $$\exists x\exists y(Px\land Py\land x\ne y)\land\lnot\exists x\exists y\exists z(Px\land Py\land Pz\land x\ne y\land x\ne z\land y\ne z).$$ ...
Martín-Blas Pérez Pinilla
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For exactly two, you could also use $\exists x\exists y\forall z(Px\wedge Py\wedge x\ne y\wedge(Pz\to(z=x\vee z=y)))$ – bof Mar 28 '14 at 10:37