cianfa72's latest activity

Statements that aren't tautologies, like ##A \rightarrow B ##, which is not true when A is true and B is false.

Ok, a well-formed formula (wff) is (syntactically) provable if and only if it is valid since we're assuming a sound and (semantically)...

Sorry, let me try to show my understanding: classic FOL is sound and complete (by Godel completeness theorem) hence a FOL wff is...

Wff's are Syntactic, i.e., strings of symbols formed by precise rules, but without any assigned meaning. Interpretations, models, are...

Sorry, could you be more explicit? Thanks.

As far as I can tell, ##|\mathbb N|## and ##|\mathbb R|## denote the cardinality of sets ##\mathbb N## and ##\mathbb R## respectively...

Yes. Yes, good point: True is used with respect to a specific model. For statements concerning all models, a different terminology is...

Yes, valid is understood as semantically valid.

Ok, you mean that a proposition is True on the elements of the topological model assigned open subset. Then if such a set is the entire...

Well, we still say that a proposition which is True everywhere is just True (or top ⊤), and a proposition which is True only on the...

In any topological model for IPL, propositions are assigned open subsets of an underlying topological space by induction starting...

No, "semantics" just means "theory of meaning". Even so you could talk of "theories of meaning", there is no way to put "semantics" into...

Ah yes, indeed thinking about it ¬P is defined as ¬P := P → ⊥ and any topological model/interpretation maps ⊥ to the empy set. Then, by...

Ah ok, so basically in logic semantic as noun doesn't exist/apply at all. Ah, so is ##\lnot P## assigned the interior of the complement...

Ok, you said semantics (plural noun) since it refers to an entire class of semantic models/interpreations and not just a single one. So...