Chris, (01)
My frustration about the state of the art of modal logic
was triggered by reading an article I was asked to review.
It is a very well written survey about multi-agent systems,
and it has good coverage of the state of the art -- of
course, with the exception of Dunn's semantics. (02)
But while reading the survey, which I will recommend for
publication (with some suggestions), I noticed the following: (03)
1. The authors say "The metalanguage approach has been
successfully adopted by a number of researchers, for
example [Turner]. However, the metalanguage approaches
have also been widely criticized [Konolige]. Instead
of choosing a metalanguage approach, most researchers
opt for a modal approach, thereby following Moore...." (04)
But if they had known anything about Dunn's semantics,
they might have noticed the option of combining modal
and metalevel approaches in an integrated system of
reasoning. (05)
2. They go on to say "However, the combination of
many modalities into a single framework presents a
significant challenge from a logical point of view." (06)
That is where Dunn's semantics shines. You can impose
a partial ordering by entrenchment over the laws to
accommodate multiple modalities. Within a given world,
an FOL theorem prover can ignore the distinctions of
entrenchment. But you also have the option of doing
metalevel reasoning about the choice of laws and doing
belief revision to resolve conflicts. (And conflicts
do arise when there are multiple agents with different
knowledge and beliefs.) (07)
3. They discuss a system that combines "epistemic (the
standard knowledge operator Ki is an S5 operator)
and dynamic logic". And they mention other systems
that use "the standard logic S5 for knowledge". (08)
Can you believe that? If the knowledge operator obeys
the S5 axioms, that implies that an agent's knowledge
remains exactly the same in every world; i.e., learning
is impossible. I wouldn't call that the "standard
operator"; a better term would be "the Bush operator". (09)
4. Another kludge: "In this semantics, both the
uncertainty about the state of the world, and that
of the action taking place, are represented in two
independent Kripke models. The result of performing
an epistemic action in an epistemic state is then
computed as a cross product" [of the two models]. (010)
A good example why levels of entrenchment for the laws
is a better approach. In another section of the article,
the authors discuss belief revision and the AGM axioms,
but they don't make the obvious connection -- it's only
obvious if you know Dunn's method. (011)
5. The real reason for using Kripke semantics: "There are
several advantages to the possible worlds model: it is well
studied and well understood, and the associated mathematics
of correspondence theory is extremely elegant. These attractive
features make possible worlds the semantics of choice for
almost every researcher in formal agent theory." (012)
In other words, it's the only one they know. (013)
6. But in the next sentence they admit: "However, there are also
a number of serious drawbacks to possible worlds semantics.
First, possible worlds semantics imply that agents are logically
perfect reasoners, (in that their deductive capabilities are
sound and complete), and they have infinite resources available
for reasoning. No real agent, artificial or otherwise, has these
properties." (014)
In other words, it's hopelessly unrealistic, but they don't know
anything else. (015)
CM> The relevant necessity in many ontological contexts is logical
> necessity, in which case S5 seems perfectly appropriate. (016)
I grant that if you want to relate proof theory to modal logic,
then S5 is useful. I've seen some attempts by Nicola to use S5
for ontology, but they showed why S5 is hopelessly unrealistic. (017)
CM> ... but also by the so-called "new" theory of reference developed
> by Kripke, Putnam, and others. (018)
Yes, another example of the "hopelessly unrealistic" sort. The
authors of that article I reviewed also mentioned this. (019)
CM> To allude to some sort of Great Academic Conspiracy that is
> selectively limiting and controlling the direction of academic
> research in modal logic is, frankly, beneath you. (020)
I never said there was a conspiracy. Never attribute to malice
what is more easily explained by ignorance. Those people are
certainly very intelligent, but they don't read anything outside
their little sandbox. (021)
CM> research on *both* sides here has been very robust and
> well-motivated. (022)
As I said that article I reviewed was very well written and it
had excellent coverage of the current research. But every system
they discussed was a toy. I would not recommend any of them for
a serious application. After 40+ years of research with Kripke
models, that is strong evidence that there must be a better way. (023)
Following is the concluding paragraph of that article: (024)
> There are far too many research challenges open to identify in
> this article. Instead, we simply note that the search for a logic
> of rational agency poses a range of deep technical, philosophical,
> and computational research questions for the logic community.
> We believe that all the disparate research communities with an
> interest in rational agency can benefit from this search. (025)
I agree. But I am writing a note to the authors that they should
widen their field of search. (026)
John (027)
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