# Expository OP on propositional logic?

**URL:** <https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886>\
**Category:** Logic & Philosophy of Mathematics\
**Created:** [September 3, 2026, 11:14pm UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886 "2026-09-03T23:14:41Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Maybe-MaybeNot](https://yyz1.discourse-cdn.com/flex007/user_avatar/www.thephilosophyforum.com/maybe-maybenot/32/1243_2.png) [@Maybe-MaybeNot](https://www.thephilosophyforum.com/u/Maybe-MaybeNot)\
**Post date:** [September 3, 2026, 11:14pm UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886/1 "2026-09-03T23:14:41Z")

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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!

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**Author:** ![Banno](https://yyz1.discourse-cdn.com/flex007/user_avatar/www.thephilosophyforum.com/banno/32/55_2.png) [@Banno](https://www.thephilosophyforum.com/u/Banno)\
**Post date:** [September 7, 2026, 9:34pm UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886/2 "2026-09-07T21:34:08Z")

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> [@Maybe-MaybeNot](#):
>
> 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.

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.

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**Author:** ![Maybe-MaybeNot](https://yyz1.discourse-cdn.com/flex007/user_avatar/www.thephilosophyforum.com/maybe-maybenot/32/1243_2.png) [@Maybe-MaybeNot](https://www.thephilosophyforum.com/u/Maybe-MaybeNot)\
**Post date:** [September 7, 2026, 10:17pm UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886/3 "2026-09-07T22:17:15Z")

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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. 😆

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**Author:** ![Banno](https://yyz1.discourse-cdn.com/flex007/user_avatar/www.thephilosophyforum.com/banno/32/55_2.png) [@Banno](https://www.thephilosophyforum.com/u/Banno)\
**Post date:** [September 7, 2026, 10:21pm UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886/4 "2026-09-07T22:21:32Z")

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> [@Maybe-MaybeNot](#):
>
> . The classical law of the excluded middle, (p v ~p), is not valid.

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](https://link.springer.com/article/10.1007/s10992-025-09808-4) or [Béziau’s Paramodal Interpretation.](https://philpapers.org/rec/OMOOBL)

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**Author:** ![Maybe-MaybeNot](https://yyz1.discourse-cdn.com/flex007/user_avatar/www.thephilosophyforum.com/maybe-maybenot/32/1243_2.png) [@Maybe-MaybeNot](https://www.thephilosophyforum.com/u/Maybe-MaybeNot)\
**Post date:** [September 8, 2026, 12:21am UTC](https://www.thephilosophyforum.com/t/expository-op-on-propositional-logic/2886/5 "2026-09-08T00:21:07Z")

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