recordings versatile contracts

We were talking about or started to talk about propositional attitudes and modal

logics and the data here is or suggests and that's exactly what we're doing is

that we in these sentences here a probably holds or it is well known that

a or something like that is these moods the red parts they actually express the

intention or attitude of the speaker towards the core sentences and we have

developed the beginnings of the logic which really has if a is what we the core

sentence box a is one kind of modality and we have a sister modality diamond a

general and all these modalities kind of falling to do those two classes and one

of the things that you should notice and but I didn't talk about last time is that

in modal logic remember why in the beginning when we were talking about

replacement by compositionality we have things like if a is equal or equivalent to b then some

and I know something about some kind of a appearing in some kind of a context and then

I could conclude at the same position P now that doesn't hold for propositional attitudes

anymore right it is not the case that even if the evening stars the morning star is Venus it is

not well known we know that it is well known that the Venus is the planet but it might not be well

known that the evening star is a planet and maybe even less known that Hesperos is a planet

probably many people would think oh that's probably a new weight loss medicine and so being well known

and doesn't propagate over time. Some of these do. Being provable is actually something that if two things are

equivalent logically then proving one could extend proving the other just by one more step

three more steps whatever. So we're entering interesting sort of logics and the syntax is that easy

take any logic sprinkle boxes of diamonds over them and semantics is more interesting but what we

have is we have a bunch of what we call possible worlds and we have an accessibility relation

let's take that one that's R and the main idea is that we kind of have whatever logic we made

modal here we have a copy of that little logic the base logic the unmodal part of the logic or we have

one of those at every word the meaning of this can be different or can change over the worlds

okay so for instance a might be true here but a might be false there and now the idea and say

it is also true here and now we the meaning of box a is well look for the meaning of a in all of these

successor worlds there are one two three and so in here a is true in one world is false in another one so

this evaluates that's the main idea that's exactly what we're going to look at today is kind of see

whether we can automate these and also see whether we can distinguish obviously those modalities

are different so kind of have some common structure common semantics but they behave

differently when we're reasoning about them some of them I can do replacements of equals or

equivalents and sometimes I cannot okay so they must behave differently so one of the things that

kind of can change in this kind of semantics is actually what the what the accessibility relation

looks like right and if you think about just if we kind of only look at maybe this possible

world structure all right and we have a say being true here then a plus box a is something that will

be true in this structure if we only have the identity if the accessibility relation is the

identity of religion then this axiom a implied what say is actually true here so what we're going

to look at today is also can we somehow find similarity between the axioms that describe

the operational reasoning behavior of our logic and what the accessibility that might actually be

useful okay so that's what we what we essentially talked about we looked at yes we looked at a

couple of different kind of interpretations of these I think that a kind of a couple of modality

they all have fancy Greek names which nobody needs to remember which I'm going to which I did write

up anyway and they kind of essentially are forgiving ourselves examples here's the crypto

models right so the first thing on our way here is is things like temporality is a mood

right and we can imagine how things would work so if we have it if we had a we wanted to have a

modal reading of tense then we might come up with typically interval time structures right if

you say Peter is climbing Mount Everest then describes a process which is a particular kind

of an event that's kind of typically has an interval of the duration in English you can see