Discrete Mathematics

... Introduction Rules And If Li proves P and Lj proves Q, then write from Li Lj have Lk : "P ∧ Q" .. Or (1) If Li proves P , then write from Li have Lk : "P ∨ Q" .. Or (2) If Li proves Q, then write from Li have Lk : "P ∨ Q" .. ...

... Introduction Rules And If Li proves P and Lj proves Q, then write from Li Lj have Lk : "P ∧ Q" .. Or (1) If Li proves P , then write from Li have Lk : "P ∨ Q" .. Or (2) If Li proves Q, then write from Li have Lk : "P ∨ Q" .. ...

Predicate Logic

... This means that ∀xP (x) ∧ ∀xQ(x) is true. If ∀xP (x) ∧ ∀xQ(x) is true, then ∀x(P (x) ∧ Q(x)) is true. Proof: Suppose that ∀xP (x) ∧ ∀xQ(x) is true. It follows that ∀xP (x) is true and ∀xQ(x) is true. So, if a is in the domain, then P (a) is true and Q(a) is true. It follows that if a is in the domai ...

... This means that ∀xP (x) ∧ ∀xQ(x) is true. If ∀xP (x) ∧ ∀xQ(x) is true, then ∀x(P (x) ∧ Q(x)) is true. Proof: Suppose that ∀xP (x) ∧ ∀xQ(x) is true. It follows that ∀xP (x) is true and ∀xQ(x) is true. So, if a is in the domain, then P (a) is true and Q(a) is true. It follows that if a is in the domai ...

The Herbrand Manifesto

... In much of the literature, Herbrand semantics is treated (somewhat understandably) as a special case of Tarskian semantics - the case where we look at so-called Herbrand interpretations. Although the two are similar in many ways, they are not the same. First of all, in Tarskian semantics, there are ...

... In much of the literature, Herbrand semantics is treated (somewhat understandably) as a special case of Tarskian semantics - the case where we look at so-called Herbrand interpretations. Although the two are similar in many ways, they are not the same. First of all, in Tarskian semantics, there are ...