# Questions tagged [predicate-logic]

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### Is there a sentence of this form? [closed]

Is there a set of sentences Γ with no predicates besides "=" with the property that an interpretation is a model of Γ iff the size of the domain is a finite multiple of three?
37 views

### Question about v-variants of variable assignments

In Full Predicate Calculus, some variable assignment q satisfies a disjunction under interpretation U if q satisfies one or both disjuncts under U, it satisfies a conjunction under interpretation U if ...
21 views

### Having trouble translating english to FOL

Having trouble with this phrase: Any column that contains a cube contains a tetrahedron, and vice versa. I tried this: ∀x ∀y ((Cube(x) ∧ Tet(y)) → SameCol(x, y)) which is incorrect because this says ...
52 views

### Truth Value of Definite Descriptions

I'm currently studying definite descriptions in logic. My textbook postulates Bertrand Russell's view of definite descriptions, but I'm curious about other views as well (in the context of classical 2-...
59 views

### SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC

Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.): (9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula ...
287 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 ...
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-...