Re: Modal Concepts?

> On 26. Aug 2021, at 10:18, Pierre-Antoine Champin <pierre-antoine.champin@ercim.eu> wrote:
> 
> Hi Henry, all,
> 
> On 17/08/2021 11:03, Henry Story wrote:
>> Hi,
>> 
>>   I was wondering how many modal concepts could be deal with
>> in N3. Perhaps there is already a good study of those?
>> 
>> I guess we could perhaps say that Truth could be considered modal,
>> and that is already defined with log:Truth.
>> 
>> Necessity could be easy:
>> 
>> { 2 + 2 = 4 } a log:Necessity .
>> 
>> It means one could always add it to any graph, even those of one’s
>> opponents. Perhaps definitions in ontologies are like that? Perhaps not.
>> 
>> {cat color Green} log:Possible, may be a way of disproving something.
> 
> I guess we could define modalities as classes of quoted graphs, and add some axioms of the form
> 
> 
>   { {?s ?p ?o} a :Necessity } => { ?s ?p ?o }.
>   { ?s ?p ?o } => { { ?s ?p ?o } a :Possibility }.

That seems right, yes.

> 
>   { ?f a :Necessity; log:includes { ?s ?p ?o }} => { {?s ?p ?o} a :Necessity }.
>   { ?f a :Possibility; log:includes { ?s ?p ?o }} => { {?s ?p ?o} a :Possibility }.

That looks right too.

> 
> but beyond that, what could we do with it?

Well for one we can start modeling what in access control areas is known as the ”:says” operator. 
It is  not a simple sentential operator like necessity and possibility, but an indexed one. 

See Martin Abadi’s "A Modal Deconstruction of Access Control Logics"
https://link.springer.com/chapter/10.1007/978-3-540-78499-9_16

It can also be represented in what is known in Functional Programming as Indexed Strong Monads
as argued in Abadi’s paper 
Access control in a core calculus of dependency
https://dl.acm.org/doi/abs/10.1145/1159803.1159839

These are really just mathematical ways of getting to the relation we have 
discussed here before namely

:Jane :says { Superman a :FlyingBeing . }

The indexed strong monads are indexed on Agents (eg. Jane) and the 
context is what is between the `{ }` and there are rules about
what can and cannot be brought into that scope. 


> I am not an expert in modal logic, but my intuition is that without a proper negation, that won't bring us very far...

I thought we did have negation, with log:Falsehood. But I can’t find it on the cwm builtins.
I think I did see it in the cwm code examples though.

In any case it is needed on the web, for an agent to be able to express disagreement on some topic
with another. Well perhaps we can get relative disagreement with a 

agent :rejects { … }

That would be a modal form of falsehood, that would not be as strong as log:Falsehood 
by tying it to a perspective. It is modal because in a way that is what modal logic does
it moves relativists Truth and Falsehood to worlds.

> 
>> Two that are particularly useful in computing are SHOULD and MUST,
>> as they are used by ietf and w3c specs. It would be nice to at least
>> be able to explain what kind of concepts those are. They somehow
>> seem related to a goal Something MUST be done - if a goal (e.g. communication)
>> is to be achieved.
> It's an appealing notion, but could you develop it a little?

I think those two are actually quite far beyond what could be expressible in N3.
David Lewis in Counterfactuals 1973 gives an analysis of ”ought” in terms of ideal
worlds (towards the end of the text). The difference with those modalities is that
the ”actual” ideal often does not contain the world from which the agent is speaking.

Ie. 

if John :believes P
then John things the actual world is an element of P.

but if John thinks one ought to P
then one cannot deduce that John thinks the actual world fits the state of affairs described by P.

Still it is worth thinking about that.

Henry

>> 
>> 
>> Henry Story
>> 
>> https://co-operating.systems
>> WhatsApp, Signal, Tel: +33 6 38 32 69 84‬
>> Twitter: @bblfish
>> 
>> 
> <OpenPGP_0x9D1EDAEEEF98D438.asc>

Henry Story

https://co-operating.systems
WhatsApp, Signal, Tel: +33 6 38 32 69 84‬ 
Twitter: @bblfish

Received on Thursday, 26 August 2021 09:32:31 UTC