m4farrel: Must stories be a sequence of *logically* connected moments? What about, if, somebody with a mental illness was writing a story in first person? Would a first person account of a mental health story still be logical, w.r.t. some logic, but perhaps derived from a set of beliefs that don't reflect reality, etc? Mental health episode, I guess.
Your favourite psychologist answers: Not necessarily. There are several ways in which a mind may go wrong. It may reason perfectly, but take implausible assumptions that nobody would think about ("The box disappeared because the aliens took it away. Of course the door is closed: they used their high-dimensional pathways!"). The logic may be just flawed, not following any rules of logic ("The aliens took the box. Ghosts are just too busy fabricating lies."). Maybe the basic facts are true, but the subject is unable to focus and tell a consistent story ("They threw it away. He gave them the keys. Oh, my, he wanted the box. But it is now lost in the gutter. So they opened the door at night!"). I will try and find some more descriptions of accounts for the mentally ill.
One of them is A is possible, [inaudible question at 10:00] ok, so there's many different that Logic can be used, the particular correspondences I'm talking about are the ones that Bob's talked about earlier, where if you proofs [???10:27] in the language as programs.
[???: question inaudible 11:30] application do you mean ... only one thing can have access to ... at once ... so like the application ... ?
... [???: inaudible answer],Pi calculus.
So that A is possible actually corresponds to something, it's called lax logic and the computational phenomenon is what you might want to call generic effects.
Claudia DI don't know if [???] column here for what happens when you do this algebraically but it is called a monad.
If you want to think about a logic in between capture what a monad is then what you need to stu...[??? 12:37] is for the idea that you have a judgement that is possible rather than it is true.
Another one is A is valid that corresponds to a modal logic and a certain interpretation of validity and that corresponds to something which is runtime code generation.
Another way to think about it is, you have a [??? 13:10] concept in the language and you have any val construct in the language.
So this is just to give you some examples that show it's very important that many different logics [??? 13:23]...sed to catch various computational phenomenons and the way that we capture them is by appropriate judgements.
And the kind of a notion of a proposition is somewhat parametric over which thing we're looking at. Now if you want to capture and apply the ideas we are giving you in these first two lectures you really have to understand in detail how you actually define a logic.
Because if you do it wrong, then the logic doesn't really make sense and the computation interpretation is off and things don't really work together the way they should.
Therefore I'm going through this very slowly. Other questions on these examples?
I think I will probably talk at least about this one, about the connection between possib??? [???] and monads. There are references for the other ones. You can look these things up.
[??? unintelligible question 14:15 ]... is there much to learn about the last modal logic? ???
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Modal logic is kind of a very broad collection on things, saying that different modes of truth, in my terminology I would say there are different judgements, that's what I would say.
So traditional logic is just concerned with the judgement of truth, or maybe with the judgement of falsehood, and in modal logic when this [...???] more refined notion of judgement, like K knows A or A is true in time T