propositional

> The double-negation holds in propositional logic Double-negation isn't a proposition, so don't know what this means.

Some examples of this are propositional logic and linear logic are decidable, whereas the halting problem and nonlinear logic are not.

I guess it should be an Exclusive OR, although I'm not sure that is allowed in propositional logic.

The early Stoics knew propositional logic, and their successors didn't until the mid-19th century.

At first the CHC was made to work for propositional logic only, i.e.

The statement could be expressed in propositional or first-order logic depending on the expressiveness required (but of course there is a complexity trade-off).

I think the best we can hope for is free, high quality, approachable instruction in propositional logic.

I don't see any other propositional logic axioms we can apply to achieve the same result.

Is it a propositional disjunction, or is it a non-disjoint union type?

Exclusive or, being a logical relationship, is allowed in propositional logic.

Typically that is some variant of a propositional resolution proof system.

> correspond to propositional logic So, by Type Systems we mean a Heyting Algebra?

There is no propositional content; there is very little thought involved at all; it's a default "meh" position that is more accurately labelled "laziness."

By the way, constantly talking in terms of "fallacies" (especially these informal ones, as opposed to actual fallacies of propositional or predicate logic) just makes you sound like a petulant 15 year old.

For example, in Programming Language Theory it's amazing how many different notions of "equal" there are (isomorphism, definitional, judgemental, propositional, extensional, etc.).

Finally, some basic thinking about propositional logic can really help to elevate your knowledge above simple boolean expressions, so that you can start to think of "foralls" and "there-exists" symbols, especially when you start to talk about type theories or logic programing.

Propositional logic is a very weak system; I don't think it can state the Riemann hypothesis.