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 D
I 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.

- [col1:
**judgements**] [col2: **logics**] [col3: **computational phenomenons**]

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? ???

People are not really looking at ???

Sound specific for ???

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 **

[up to 15:02]