On Solving the Qualification Problem - Semantic Scholar

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From: AAAI Technical Report SS-95-07. Compilation copyright © 1995, AAAI (www.aaai.org). All rights reserved.

On Solving the Qualification Problem Charles Elkan Department of Computer Science and Engineering University of California, San Diego [email protected]

ABSTRACT: The qualification problem may be the most

fundamental difficulty in formalizing common sense knowledge in general, and in formalizing knowledge about action in particular. This position paper argues that the qualification problem is intrinsicallycomputational as opposed to representational. This does not imply that explicit, formal, knowledge has no role in the production of commonsensical behaviour, but it does imply that the qualification problem cannot be solved using currently available representation formalisms. For a future representation formalism to help in solving the qualification problem, it will be vital for it to possess a context mechanism.

Artificial intelligence research has a history of wishful thinking. In the 1950s the hope was that the right heuristic search algorithms, if only they could be found, would suffice to explain and duplicate human problem-solving skills. Another hope arose after it became clear that large quantities of initial knowledge were necessary in problem-solving: that this knowledge could be acquired by a natural language understanding program which could be written after relatively simple principles of syntax and semantics were elucidated. Neither of these hopes has been realized, but wishful thinking springs eternal, and many researchers still hope that it is possible somehow to obtain the benefits of possessing a large mass of common sense knowledge without actually stating all the knowledge formally.1 Lenat and Guha call attempts of this nature “free lunch tries” [Lenat and Guha, 1990]. In the knowledge representation community we are justifiably skeptical of the free lunch tries of others, but we are still lured by a hope of our own. This is the hope that the right nonmonotonic logic can, in and by itself, solve dilemmas of common sense reasoning. The two bestknown examples of the inferences that nonmonotonic logics are supposed to sanction concern a canary and a turkey:

 “Tweety is a bird; therefore Tweety can fly.”  “Loading then shooting kills Fred; therefore loading, then waiting, then shooting kills Fred.”

The desire for a formalism where these inferences are legitimate is the desire for a formalism where appropriate conclusions can be drawn even in the absence of full knowledge of all relevant circumstances. The qualification problem, as commonly understood, is that in almost all common sense scenarios, it is impossible to state all relevant circumstances. In other words, general rules of common sense are always incomplete.2 However many preconditions have been taken into account in the formalization of a rule, one can think of further preconditions whose truth influences the truth of the consequent of the rule, so the formalization should mention even more antecedents. The first example of nonmonotonic reasoning above illustrates this phenomenon. The general rule that birds fly in actuality has many unstated further antecedents, such as that the birds in question are not penguins. The second example of nonmonotonic reasoning above is commonly viewed as illustrating the frame problem, but the frame problem can be viewed as a version of the qualification problem: here for example, loading then shooting only kills Fred if many other unstated assumptions are true. In a nutshell, the frame problem is that one only wants to state the conditions under which a property of the world does not persist, leaving the conditions under which it does persist unstated. We can distinguish weak and strong variants of the qualification problem. The weak form is the case where the unstated additional relevant antecedents could in principle be made explicit, while the strong form is the case where these antecedents could not plausibly be enumerated even in principle. An instance of the frame problem is an instance of the weak qualification problem if the conditions under which world properties persist can in principle be enumerated; if they cannot, one has an instance of the strong qualification problem. The conventional intuition behind the search for a nonmonotonic logic as a solution to the qualification problem is that rules of common sense express “default” truths. According to this intuition, the rule that “if you turn the key, the car starts”, which ignores further preconditions that the battery should not be dead, the fuel pump should not be clogged, the gas should contain no sugar, and so on, should be formalized along the following lines:

1

“The fundamental issues of AI can only be solved with an orchestrated application of fuzzy logic, neural networks, genetic algorithms, and probabilistic reasoning.” [Vadiee and Jamshidi, 1994]

2 This general rule itself is also incomplete. Some rules of common sense are definitional and therefore can be specified completely.

no unstated precondition can defeat the rule. For any knowledge base including (1), if the knowledge base entails turn-key and :dead-battery and :clogged-fuel and :sugar-in-gas then it entails car-starts with certainty. The statement of rule (1) excludes all potential qualifications except those stated explicitly. Other nonmonotonic logics with similar minimizing semantics behave similarly. Yet the qualification problem is precisely that the common sense rule behind (1) does have unknown preconditions.5 Leaving open the question of the representational adequacy of the default logic approach to solving the qualification problem, it is still apparent that the solution is computationally inadequate. The real issue from a practical perspective is not so much how to enumerate the preconditions that are relevant to a rule, but when to assume that they hold or do not hold. Consider reasoning with a knowledge base containing (1). Before the default logic rule is used, the falsity of all defeating preturn-key & ˜dead-battery & ˜clogged-fuel conditions must be checked one by one. This computational & ˜sugar-in-gas -> car-starts expense is precisely what a solution to the qualification problem should avoid. Certainly when a human turns an ignition default-false: dead-battery, clogged-fuel, key and expects a car to start, he does not devote any time to sugar-in-gas enumerating reasons why the car may not start.6 Assertions of this type can be directly translated into assertions If the computational dimension of the qualification probin default logic [Reiter, 1980]. The example above becomes lem is the most fundamental, then perhaps explicit logical knowledge has no place in the production of commonsensical turn-key : :dead-battery :clogged-fuel :sugar-in-gas behaviour? Several researchers, for example Brooks [1987], (1) have indeed reached this conclusion. Typically they advocar-starts cate improvisation instead of logical reasoning about action. There is no need to state explicitly that dead-battery is false Moreover, there is wide agreement that the traditional view by default, because the semantics of default logic makes it of planning (dominant from the work on STRIPS [Fikes et false automatically, if it can consistently be false. The same al., 1972] to the development of TWEAK [Chapman, 1987]) applies to clogged-fuel and so on.3 is no longer tenable, because of intrinsic uncertainty in the As a first approximation, we can identify three dimensions environment and the need to react quickly to events. of adequacy along which a candidate solution to a common However, the search for some sort of logic to use in formalsense formalization problem can be judged [Elkan, 1991]. izing common sense knowledge and reasoning about action is In summary, the solution is intuitively (philosophically) adstill a sensible enterprise. Even a weak ability to forecast the equate if what is stated is clear, and clearly correct. The consequences of actions before undertaking them can clearly solution is representationally adequate if it is concise, modube adaptive. An improvising agent is doomed to choose aclar, and it can be combined without change with the solutions tions whose optimality is only local, and in many domains, to other common sense formalization problems. Finally, the goals can only be achieved by choosing actions whose role solution is computationally adequate if ecologically important is indirect. Also, the biological evidence is that declarative, problems can be solved efficiently using the solution.4 propositional knowledge does play a major part in directing According to these criteria, the solution outlined above to human behaviour. Neuroanatomical research has identified a the problem of formalizing common sense knowledge about distinct region of the brain that is responsible for acquiring when a car starts is inadequate. It is inadequate on the intudeclarative memories of facts and events [Squire and Zolaitiveness dimension because all potential qualifications to the 5 basic rule “if you turn the key, the car starts” have been made An unknown precondition is very different from a precondition whose truth is unknown. It is of no help in solving the qualification explicit. The semantics of default logic formally entails that defaultrule129: turn-key -> car-starts dead-battery cancels default129 clogged-fuel cancels default129 sugar-in-gas cancels default129 ... Specifying preconditions separately from a basic rule unfortunately involves reifying rules, which is technically difficult. Even in a second-order language where quantification over predicates as well as individuals is allowed, it is not possible to assign a name such as default129 to an entire sentence, and to write other sentences using the name. Another way of stating default knowledge is therefore used in practice. In this approach relevant preconditions are brought into the formalization of the common sense rule, and these preconditions are stated to be typically false using a special operator of the nonmonotonic logic. Informally, the following is written:

3

The fact that no axiom need be written to require that a proposition-symbol be false by default implies that no propositionsymbol can be introduced that is not false by default. This is a significant apparent limitation on the expressiveness of default logic. Recent work by Gelfond and Lifschitz [1991] and others has been directed towards lifting this restriction, allowing the writer of a set of axioms to choose for each atomic literal whether it should be false by default or unknown by default (which is the semantics of a newly introduced literal in standard monotonic logics). However the resulting logics are technically no more expressive than standard default logic. 4 “Behind all logic and its seeming sovereignty of movement, too, there stand valuations or, more clearly, physiological demands for the preservation of a certain type of life.” [Nietzsche, 1886]

problem to be able to choose whether a precondition should have truth-value false or unknown by default. If the truth of a precondition in the formalization of a common sense rule is set unknown by default, then in the absence of further information (which is the normal case) the rule will not be usable for drawing any inferences. And the strong version of the qualification problem is that many relevant preconditions cannot be stated at all in advance. 6 It is not enough to reply that the preconditions can be checked once and for all, in a preprocessing phase. Each episode of trying to start a car actually involves different instances of the propositions dead-battery etc. If a well-accepted first-order variant of default logic existed, it would have been used above, but one of the technical difficulties with default logic (which other nonmonotonic logics share) is that it is difficult to extend the semantics from the propositional case to the full first-order case.

Morgan, 1991]. Given that it is useful to search for an appropriate logic for formalizing common sense knowledge, what features should this logic possess? The analysis above suggests that the logic should possess a context mechanism. The preconditions that may defeat a common sense rule are assumptions on which the rule’s validity rests. The typical case is that all these assumptions do hold. This typical case should be handled computationally without enumerating all the assumptions, which can be achieved by treating the collection of assumptions as a unit. A collection of assumptions is a context. The notion of context is intrinsically dynamic. One enters a context, one remains in a context, one changes context if the current context is untenable. Traditionally, logic has had a static bias, but some logicians are developing dynamic formalisms where contexts play a central role [van Benthem, 1991]. The motivation of their work is linguistic: to model how a speech act changes the information state of a hearer. What is suggested here is different in two ways, but should lead to formalisms with similar technical features. The two differences are first that environmental events, not speechacts, are what changes the information-state of an agent, and second, that the state of an agent to be modelled is its “available” information rather than its entire long-term knowledge.7 Contexts are of course not a new idea in artificial intelligence. The idea of relying on assumptions that are left unproven appears in [Doyle, 1983; Feldman and Rich, 1986] and elsewhere. Truth maintenance systems have been called context maintenance systems, and are widely used as a pragmatic solution to the qualification problem [de Kleer, 1986; Petrie, Jr., 1989]. A context mechanism is an important recent addition to the CYC system [Guha and Lenat, 1992], and there is recent work on formalizing contexts [Buvac and Mason, 1993]. No doubt there are many further features that a logic for formalizing everyday declarative knowledge should possess, but a context mechanism permitting solutions to the qualification problem to be implemented is already a substantial research topic.

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One of the prominent differences between biological and artificial memory systems is that the short-term retrieval strength of memories decays rapidly in humans and animals. A recent theory of memory suggests that this phenomenon is adaptive: for an organism whose reasoning resources are limited, it is advantageous for only a subset of its long-term knowledge to be immediately available, with recent experiences determining which knowledge is available [Bjork and Bjork, 1992].

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