on Thu. Dec. 27, 2007 at 11:28 AM, John F. Sowa wrote: (01)
JS>I agree with the points that Chris and Pat made about contexts,
> but I'd like to add a few comments.
>
> JB>> I had thought that time was yet another type of context. Is it
> >> different somehow?
>
> PH> You CAN treat time as a context, if you like contexts. But that is
> > not the only way to tackle a logic of time: the modal temporal logics
> > pre-date context logics by about 60 years.
>
> I agree. A context approach to time can be reduced to a noncontextual
> approach by adding an extra argument for time to every relation.
> For example, consider the sentence
>
> At time t, the cat Yojo was on a mat.
>
> In a context approach, you could translate that to a conceptual graph
> of the following form:
>
> [Time: *t]<-(PTim)<-[Situation: [Cat: Yojo]->(On)->[Mat] ] (02)
And this is one of the main attractions for me about Conceptual Graphs. The
enclosing 'Situation:' concept looks a lot like a context to me. But CL and
thus CGIF are not "context logics". What does it take to make a logic a
context logic if not just that you can express such contexts? Also, the
above CG is not written in CGIF, is it? In particular, the "<-" syntax for
arcs is not a part of CGIF, as far as I can tell. (03)
The other big attraction of CGs to me is the attractive possibility that the
graphical display of CGs may facilitate the solution of certain types of
reasoning problems. I am particularly interested (for no particular
practical reason, just am) in the possibility of reasoning about the kind of
knowledge problems described in "Reasoning About Knowledge" by Fagin, et al.
http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8240 (04)
[Person:*j]<-(KnownBy)<-[Knows:[[Person:*h]<-(KnownBy)<-[Knows:[[Person:*j]<-(KnownBy)<-[Knows:[Cat:Yojo]->(Named)->["Yojo"]]]]]] (05)
If I did this right, it means: a person *j knows that a person *h knows that
he, *j, knows that Yojo the cat is named "Yojo". Textually, it gets very
complicated to look at. Would it be simpler for a human if this was visible
graphically? And does it make any difference to a machine? Do you think
there is any parallel in automated processors of the advantages to humans of
graphical reasoning? (06)
John Black
www.kashori.com (07)
> But the same sentence could be represented with the following CGIF
> statement, in which the dyadic relation On is replaced by a triadic
> relation that has an extra argument for time:
>
> [Time: *t] [Cat: Yojo] [Mat *x] (On Yojo ?x ?t)
>
> Following is the equivalent CLIF:
>
> (exists ((t Time) (x Mat)) (and (Cat Yojo) (On Yojo x t)))
>
> This method might look simple for such a short sentence. But with
> many different time points with many relations, the context boxes
> group related information in a more readable notation. Whether that
> grouping is simpler for reasoning depends on the type of problem.
>
> I'd also like to recommend some references. The first is to the work
> of Arthur Prior, who developed the modal approach in detail. Following
> is a brief article about Prior and his work:
>
> http://plato.stanford.edu/entries/prior/
> Arthur Prior (Stanford Encyclopedia of Philosophy)
>
> Another article:
>
> http://www.hum.au.dk/ckulturf/pages/publications/ph/life.htm
> Per Hasle: Life and Work of Arthur N. Prior
>
> Interesting quotation from above:
>
> "I think I'm right in saying that Arthur initially accepted
> Russell and Whitehead as establishing the parameters of modern
> logic; developed doubts as he read more ancient and medieval
> logicians, and then sought to formalize a tensed logic which
> would deal with tensed statements."
>
> One source that Prior probably read was Ockham's _Summa Logicae_,
> which was finished around 1323. Part II presents Ockham's theory
> of propositions, which states truth conditions for Latin sentences,
> very much along the lines of Tarski's model theory. Ockham isn't
> as formal as Tarski, but his book is a very readable introduction
> to the approach. See
>
> Ockham, William of, _Ockham's Theory of Propositions_,
> translation of Part II of Ockham's _Summa Logicae_ by
> A. J. Freddoso & H. Schuurman, University of Notre Dame Press,
> Notre Dame, IN, 1980.
>
> Unlike Tarski, who covered only first-order logic, Ockham stated
> truth conditions for modal, temporal, and causal statements.
> Ockham's approach to those subjects was far too brief to cover
> all the issues and problems, but it was undoubtedly one of the
> inspirations for Prior's work.
>
> I'd also like to mention a very good analysis and comparison of
> several different formalizations of time:
>
> Gergely, Tamás, & László Úry (1991) First-Order Programming Theories,
> Springer-Verlag, Berlin.
>
> Unfortunately, the list price is $125, but Powell's bookstore, which
> I recommend, has a copy for $11.
>
> Gergely and Ury present temporal logics and dynamic logics. But they
> argue that the simplest and most general approach is a first-order
> method that quantifies over time. I agree with them, although I admit
> that the other approaches are useful for some purposes. For example,
> certain proofs may be very short in a modal approach to temporal logic,
> but more complex in FOL.
>
> John Sowa
> (08)
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