Expository OP on propositional logic?

Logic & Philosophy of Mathematics
1

I’m new to TPF. Apologies if this is the wrong category.

I’ve been working for some time on a system of propositional logic melding classical 2-valued logic with S5. It’s finally coming together.

Now I have the problem of how to publish, since I’ve been outside academia for almost 50 years. A TPF post would need to be rather long and have several parts.

Is this sort of post appropriate here? Should I put it on a website and announce it here? Cross my fingers and send it to JSL? Any & all comments or suggestions are very welcome!

2

No relies, perhaps because the details are a bit scant.

S5 is a modal system that is usually interpreted using a 2-valued logic… So what have you done that is novel? Looks to be the textbook version of S5.

3

Thanks for replying. There’s plenty of novelty. I was careful to say “melding.” It’s a system intended for formalizing theories, like that of partial recursive functions, in which some statements lack a truth value. The classical law of the excluded middle, (p v ~p), is not valid. This is not your grandparents’ S5!

Details about the system are scant in this post, definitely, as you say. But I didn’t want to write a lengthy exposition only to be told it didn’t belong here. Since no one has said that, I’ll start separate threads setting out the whys & wherefores, model theory, proof theory and the rest of that fun stuff. Please stay tuned. :laughing:

4

Then it’s not a classical logic, in the usual sense, but a paraconsistent logic. A paraconsistent interpretation of S5? There are a few of those. Have you looked at them?

Jaśkowski’s Discussive Logic or Béziau’s Paramodal Interpretation.

5

Thanks for your interest. Perhaps we can return to paraconsistent logics later in our discussion.