May 8, 2016 · Scott's axioms imply the " modal collapse ": every true statement is also necessarily true: $$ \forall \phi (\phi \to \square \phi) $$ and it is said that this modal collapse is an …

Jun 26, 2022 · Equivalent of Post-completeness for modal logic S5; any stronger system leads to modal collapse. Ask Question Asked 3 years, 5 months ago Modified 3 years, 5 months ago

6 I think dismissing an argument that stands foursquare in a 900 year tradition of logical discourse as a 'strange apparent aberration' is a little questionable. Anyway, it's worth noting that the argument's …

Sep 19, 2018 · There are logics that reject the principle of explosion: paraconsistent logics and in particular minimal logic. Such logics make it possible to distinguish between inconsistent theories …

Equivalent of Post-completeness for modal logic S5; any stronger system leads to modal collapse. I've heard before that classical propositional logic is Post-complete, for example, see this answer.

Nov 23, 2023 · Modal collapse is not in the deductive closure of S5, so asserting the presence of a sole sufficient operator has caused us to lose some models of our equation theory.

Oct 8, 2020 · In the answer provided to the question https://mathoverflow.net/questions/296440/modal-collapse-upon-addition-of-the-law-of-the-excluded-middle-to-an-intuitionis, a proof is given, showing …

Mar 21, 2021 · Equivalent of Post-completeness for modal logic S5; any stronger system leads to modal collapse. A I

Equivalent of Post-completeness for modal logic S5; any stronger system leads to modal collapse. I've heard before that classical propositional logic is Post-complete, for example, see this answer.

Sep 28, 2023 · Triv is a system that corresponds to modal collapse, so it is not very useful. For any P: MP, P and LP all hold, or M¬P, ¬P and L¬P all hold.