Simulating Non-Deductive Reasoning

ABSTRACT

This paper is intended to draw attention to a literature in Philosophy that would be of great use and interest to research­ ers attempting to simulate non-deductive reasoning. Two models of such reasoning are discussed, and the kernel role of the concept of explanation common to them both is revealed. Finally, the relevance of the conceptual insights to computing by appealing to Scriven's comprehension theorem which facilitates a link between the concepts of explanation, understanding and processing efficiency under certain constraints.

l. Introduction

A fairly recent survey found that researchers in Artificial Intelligence considered Philosophy of more immediate relevance to their work than Psychology (Newell, 1980). This is a plausible atti­ tude toward a discipline that is tradi­ tionally preoccupied with the mental, with knowledge and with reasoning. It is a reasonable hope that the body of philo­ sophic ruminations about these domains, though are univocal, will help the formu­ lation of precise characterizations of the properties intelligent programs are sup­ posed to exhibit, i.e., specifications of the behavior to be simulated.

The first two of the three philo­ sophic preoccupations mentioned above have fairly old titles, philosophy of mind and epistemology, respectively. The third concern, the characterization of reasoning properly belongs to logic. In what fol­ lows, however, I wish to call attention to and draw upon a literature that is not precisely at home in any one titled field of philosophy.

The literature in question is one concerned at a conceptual and not a psychological level with the characteriza­ tion of reasoning, ordinary reasoning from

James w. Hearne

Hughes Aircraft Company

evidence to hypotheses, actions and pred­ ictions, which is by and large non­ deductive. Attempts to simulate such rea­ soning typically devolve to attempts to reconstruct non-deductive reasoning as a deductive system with exotic properties such as probabilistic truth values or non-monotonicity. An. examination of the philosophic literature reveals several important abstract traits which programs simulating intellection must reckon with that are probably incompatible with a straightward deductive system. It is only by avoiding deductive reconstruction that salient features of such reasoning such as its value dependance and its intimate con­ nection with concept of explanation is revealed.

2. Describing Non-deduction

It is convenient to describe non-deductive reasoning as a kind of departure from full deduction. This is done by posing some paradigm argument schemes appropriate to given problem areas and then describing the stratagms that ensue when one of the premises of the model argument is false. I will be concerned with two such para­ digms, one for evidential reasoning and one for reasoning to actions.

3. Evidential Reasoning

The paradigm argument is,

(1) X explains (why) Y (is true). (2) Nothing but X would explain (why) Y (is true). (3) Y is explained by something or other.

(C) X ( is true)

Roughly, the context in which the paradigm is relevant is one in which some fact Y inviting explanation is known and some other fact X, if true, would explain Y. With premises (1), (2) and (3) the argument to X is a deductive one. In the normal life of reasoning, something like (1) is frequently known and (3) is simply presupposed (though it is false in some d omains such a Quantum Mechanics). How­ ever, (3) is almost always false, because there are always explanations that rival the o ne isolated in the conclusi on.

In response to the fact that (2) is false reasoners engage in various stra­ tagms designed t o isolate some conclusi o n from the other candidates as clearly better or more plausible. Such strategies exhibit a structure at least as compli­ cated as the f o llowing method of p ro­ cedure.

• (l) Articulate (fo rmulate, identify) a fact (or facts) inviting explana­ ti on.
• Articulate (& et cetera) facts (hypo theses) which~if true, would explain the facts gathered in (1).
• Rank the yieldings o f (2) in order of plausibility.
• {4) Articulate (& et cetera) facts which, if discoverea, would alter the order provided in (3), or continue.
• Either goto (2), (3) or continue.
• Infer, pick, go with, the c onclu­ sion at the top o f the plausibility ranking pr ovided most recently in ( 3) ·

Thus, some fact, such as a noise in the next room, may initiate step (1), fol­ lowed by step (2), the formulation of explanations of the fact, f o llowed in turn by (3), a ranking of the explanations in order of plausibility. One may then a r ti­ culate some fact, which if discovered wo uld clearly alter the ranking. One must either return to the formulation of new explanations or t d (4) to determine whether any o f the facts devised in (3) obtain and alter the current ranking accordingly. Eventually, the method of procedure will be abandoned, in a sense t o be discussed anon, by acting on the c on­ clusion at the top of the plausibility ranking.

The method of procedure is not an algorithm, since the branching at steps (4) and (5), is the point at which aban­ donment (jummping out) occurs, is not deterministic. This is a reflection of the fact that the reasoning is non­ deductive, i.e., though the argument from P to Q may be a perfectly good one, the denial of Q does not force the denial of P. This is due to the fact that P is simply the best of a collection of r ival con­ clusi ons all o f which must be {1) c ompati­ ble with the evidence--since the evidence supports each-- and {2) incompatible with one another, since they can't all be true.

4. Reasoning t o Actions

A seco nd s or t of reasoning is reason­ ing t o actions, represented by the f o ll ow­ ing paradigm:

• {1) The r e is a reason t o do X.
• {2) There is no reason to do o the r than X.
• {3) One ought t o do s omething or o the r .

(C) One ought to do X.

As before, premise (1) is frequently simply known, (3) is supplied by the c on­ text, but (2) is usually false, since rea­ sons to do o ther than X are usually abun­ dant. The falsity of (2) is met by an appr opr iate abstract rational procedu~e who se object it is t o iso late one act1on as better supported than any o ther. In the interests of efficiency, we shall not rehearse the procedures (which can be rather complicated) we will use the method o f pr ocedure f or evidential reasoning as grist f or further investigati on.

5. The Problem of Detachment

The procedures f or rationally responding t o the absence of deductive validity are not algorithms in a strong sense. In the procedure for evidential reasoning, steps (4) and (5) are non­ deterministic. Most important, there is no provision for halting, i.e., the instructions do not determine when to jump out of or abandon the procedure and believe the conclusi on, or do the action, currently best suppor ted. Thus is the problem of detachment, the problem of articulating a criterion with which to 'detach' ~ conclusion (action or belief) from the rationcinati6n it is embedded in.

Foremost is the problem of character­ izing what it means to detach. In the case of reasoning to action this is fairly straightforward; one detaches by doing the action best supported. In the case of evidential reasoning, the characterization requires greater subtlety. For present purposes, we will use the unattractive expression--for which I have found to substitute--"go with". To detach is to go with the current best supported hypothesis or conclusion.

Detachment can be forced by cir­ cumstances. This is it may be rational to go with a conclusion because circumstances demand going with some hypothesis or other and rationality demands that this be the hypothesis at the top of the plausibility ranking. More importantly, detachability is a value dependant trait, as is shown by an example originally constructed by Scriven. Suppose that one wishes to haul a bail of hay to an upper story loft with and a rope and pully and there is some evidPn~P AS to whether the rope is strong enough. One can imagine the kinds of evi­ dence marshalled to elevate the conclusion that the rope of sufficient strength to the top of the plausibility ranking. One may inspect the rope for defects, give it a strong yank, et cetera. Imagine the evidence that would settle the matter. Now imagine the item to be hoisted to be no~ a bail of hay but one's daughter, Whlch we may assume weighs the same as the bail. One will probably observe that the evidence imagined to be sufficient for hay is inadequate to the question of hoisting one's daughter. What this reveals is that the value component in non-deductive rea­ soning, that what it is rational to detach--conclude--non-deductively is in part a function of one's values. This is of course untrue of deductive reasoning which is valid or not independent of the consequences of being wrong.

6. The Role of Explanation and Under­ standT"i1g

The two species of reasoning for which model arguments were provided share in common the concept of explanation--and its correlative concept, understanding--at their core. In the case of evidential reasoning, we judge that X is evidence for Y if and only if Y explains x. The role of explanation in reasoning to actions is less obvious. In general, to say that a person P does an action A for reason R means something like,

1. P knows (or believes) R, and
2. The fact that P knows

(believes) R explains why P does A.

Thus, a reason is a fact an agent's knowledge of which would explain the his performance of some action.

What this is implies is that one glo­ bal constraint on reasoning is explanatory coherence, or coherence of understanding. That is, plausibility judgements are driven by perceptions of the degree to which a given conclusion candidate coheres explanitorily with the remainder of one's of comprehension are automatic conse­ quences of information processing stra­ tegies designed to maximize efficient storage and retrieval while interacting with an informationally rich environment. Indeed, according to this view, comprehen­ sion is the disposition or capacity for effective storage and retrieval under the constraint of the impossibility of total storage; that is, maximizing storage and retrieval in an environment so rich that complete storage is impossible.

Thus, one can identify something like a connection between something computable and the apparently vague concepts of explanation and understanding that lie at the core of non-deductive reasoning--if the described paradigms are characteris­ tic. In any case, the relevance of the philosophic literature on non-deductive reasoning that does not reconstruct such reasoning deductively is I hope made more plausbile by these remarks.