I designed some new modal operator symbols. phi implies downnecessary uppossible phi phi implies upnecessary downpossible phipic.twitter.com/j5EJMNimkc
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Oh yes, I am using these in the generic multiverse of set theory, where some modalities go up to larger universes and others go down.
For example, my implications are valid for these semantics. A similar validity holds for future/past in temporal logic.
If phi is true now, then every past moment was such that it could become true. And every future moment will be such that it once was true.
This sounds fun
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