Propositional logic vs predicate logic: examples? About the difference between the propositional logic and the (first order) predicate logic->


*

*can you give me one or more remarkable examples which underly the differences and the similarities between the two?

 A: The obvious difference is that predicate logic allows for quantifiers. E.g.


*

*Propositional: $p\implies p $

*predicate: $\forall x:p(x)\implies p(x) $

A: In propositional logic the "atoms" are propositions, whith them you can always build new ones using the logical conectives, for example you could have a proposition $p$ which means "there is a dog in Luca's house" and another propositio $q$ which means "Luca is Sandra's boyfriend", now you can say "there is a dog in Sandra's boyfriend's house" in the language of propositional logic in the following way: $p \land q$.
In predicate logic you can "break" those "atoms" and work with the "subatomic particles", and so this form of logic allows us to analize the internal structure of the propositions. Now you can use quantifiers, terms, relations and functions. You can define, for example: $d(x)$ means "x is a dog" $h(x,y)$ means "x is in y's house" $b(x)$ means "the boyfriend of x" and finally define Sandra as the constant $s$, now your proposition would be: $$\exists x (d(x) \land h(x,b(s))$$
