Questions tagged [predicate-logic]

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1answer
278 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
2
votes
0answers
38 views

What are some benefits of a second order logic?

I have read that a second-order logic can help one define equality by quantifying over all predicates such as what is done in the following definition: (x=y):⟺[∀P:P(x)⟺P(y)] By contrast a first-...
0
votes
2answers
73 views

How does one tell if logical expressions are equivalent?

How do I check if these expressions are equivalent? ∀a,b [P(a) ∧ ¬R(a) ∧ S(b)] → G(a,b) ∀a [(P(a) ∧ ¬R(a)) → (∀b [S(b) → G(a,b)])]
3
votes
2answers
290 views

Are there paradoxes involved in allowing for an unrestricted domain in predicate logic?

I've put some thought into this, and just want to make sure I'm on track, or if I need to be corrected. Basically, my answer is this: Yes, you need to always specify a domain when formalizing into ...