[FRIAM] abduction and casuistry

Thu Aug 22 20:50:42 EDT 2019

A good word to generalize implication, causation, etc. Is entailment.
There is an old book by Anderson and Belnap which may shed some light on
abduction.  It's title is The Logic of Entailment.

I always thought that abduction had the form "If A entails B then the
presence/occurrence of B makes it more Likely that A is present/has
occurred." I don't see how that is represented by the formalism you quoted,
however.

Frank

-----------------------------------
Frank Wimberly

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Phone (505) 670-9918

On Thu, Aug 22, 2019, 11:49 AM uǝlƃ ☣ <gepropella at gmail.com> wrote:

> Maybe to give context to my hand-wavey colloquial nonsense below, I
> *really* like Gabbay and Woods' [†] formulation of an "abductive schema":
>
> > Let Δ=(A_1,…,A_n) be a *database* of some kind. It could be a theory or
> an inventory of beliefs, for example. Let ⊢ be a *yielding relation*, or,
> in the widest possible sense, a consequence relation. Let Τ be a given wff
> (well-formulated formula) representing, e.g., a fact, a true proposition,
> known state of affairs, etc. And let A_(n+j), j=1,…,k be wffs. Then
> <Δ,⊢,Τ,A_(n+j)> is an abductive resolution if and only if the following
> conditions hold.
> >
> > 1. Δ⋃{A_(n+j)} ⊢ Τ
> > 2. Δ⋃{A_(n+j)} is a consistent set
> > 3. Δ ⊬ Τ
> > 4. {A_(n+j)} ⊬ Τ
> >
> > The generality of this schema allows for variable interpretations of ⊢.
> In standard AI approaches to abduction there is a tendency to treat ⊢ as a
> classical deductive consequence. But, as we have seen, this is
> unrealistically restrictive.
>
> (Emphasis is theirs, at least in the draft copy I have.) They go on to
> assert:
>
> > ⊢ can be treated as a relation which gives with respect to Τ *whatever*
> property the investigator (the abducer) is interested in Τ's having, and
> which is not delivered by Δ alone or by {A_(n+j)} alone.
>
> In my colloquial description, Δ is the collection of old dots there at the
> start of the process and Τ is the new dot. It's open whether or not the set
> of wffs (A) are also dots or part of the connections drawn between them,
> depending on how you feel about *dot composition* (e.g. subsets of dots
> that are all very close together, so we just draw them as one big dot or
> somesuch) and scale/resolution. Rule (2) is *clearly* a rule for how the
> dots can be connected. In general, consistency is also an ambiguous concept.
>
> As always, I'm probably wrong about whatever it is Gabbay and Woods are
> saying. Any errors are mine. But maybe their words above can give some
> context for how I feel about "reasoning from particulars".
>
> [†] https://www.powells.com/book/-9780444517913
>
>
>
> On 8/22/19 8:26 AM, glen∈ℂ wrote:
> > First, did you miss Dave's contribution?  It was more on-topic than mine!
> >
> > On Rigor: Yes, there's quite a bit of what you say I can agree with. But
> only if I modify *my* understanding of "rigor". I think rigor is any
> methodical, systematic behavior to which one adheres to strictly. It is the
> fidelity, the strict adherence that defines "rigor", not the underlying
> structure of the method or system. And in that sense, one can be rigorously
> anti-method. Rigorously pro-method means adhering to that method and never
> making exceptions. Rigorously anti-method means *never* following a method
> and paying (infinite) attention to all exceptions, i.e. treating everything
> as a single instance particular, an exception. I grant that "methodical
> anti-method" is a paradox... but only that, not a contradiction.
> >
> > On monism vs. monotheism: The simple answer is "no". I'm not confusing
> the two. By reducing every-stuff to one-stuff, *and* talking about types of
> inference like ab-, in-, and de-duction, you are being (at least in my
> view) axiomatic, with a formal system based on 1 ur-element. Everything
> else in the formal system has to be derived from that ur-element via rules.
> To boot, your attempt to classify casuistry and abduction (same or
> different is irrelevant, it's the classification effort that matters)
> argues for some sort of formalization of them. A/The formalization of
> abduction is an active research topic. My use of the word "deontological"
> was intended to refer to this rule-based, axiomatic way of thinking. I'm
> sorry if that lead to a red herring off into moral philosophy land.
> >
> > On inferring from particulars: While it's true that induction builds a
> predicate around a particular, it is a "closed" set. (Scare quotes because
> "closed" can mean so much.) Abduction doesn't build predicates and any
> explanation it does build is "open" in some sense. So, I would agree with
> you that one can't really *argue* from a particular using abduction. I tend
> to think of it more like brain storming, in a kindasorta Popperian, open
> way. Any proto-hypothesis can be brought to bear on the abductive target.
> And the best we can do is play around with the abductive target to see if
> it might kindasorta *fit* into that open set of proto-hypotheses. Once you
> land on a set of proto-hypotheses that's small enough to be feasibly
> formulated into testable hypotheses, then you reason by induction over
> those hypotheses.
> >
> > In some ways, this would be very like what I, in my ignorance, think
> casuistry is. I'd argue that an experimentalist's focus on putting data
> taking in 1st priority and hypothesis formulation in 2nd priority falls in
> the same camp. So, I agree that casuistry looks a lot like abduction. But I
> don't think that that criminologist was doing either of them.
> >
> > On ontology vs. rules *and* reasoning from particulars: The
> proto-hypotheses I mention above do not have to take the form of "rules to
> apply" to the abductive target. Think of the game "connect the dots", where
> the dots are particulars and they are/can be interpolated and/or
> extrapolated by an infinite number of lines between them. On the one hand,
> more dots can make it more difficult to find a pattern that includes the
> *new* dot, but perhaps only when you're already pre-biased with a set of
> lines that connect the old dots. On the other hand, if you're rule-free
> when you look at the old set of dots *and* rule-free when you look at them
> with the new dot included, you're open to any set of connecting lines.
> >
> > Of course, in science, we do have an ur-rule ... that *all* the dots
> must be connected. So, that constrains the set of lines that connect the
> dots. And the more dots, the fewer ways there are to connect them. But
> practicality demands that we doubt at least some dots. So, we're allowed to
> throw out the weakest dots if that allows us to form more interesting
> connective patterns.
> >
> > So, in this scenario, the proto-hypotheses are really just collections
> of old dots in which the new dot must sit.  We're not reasoning from *one*
> particular to testable hypotheses. We're reasoning from the addition of
> that particular to collections of other particulars.
>
> --
> ☣ uǝlƃ
>
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