Concept Construction as Constraint Relaxation: Working Note 3. Peter Clark and Bruce Porter. Dept. CS, UT Austin.

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1 Concet Construction as Constraint Relaxation: Working Note 3 Peter Clark and Bruce Porter Det. CS, UT Austin fclark,orterg@cs.utexas.edu 1 Introduction Anyone who's tried building a knowledge-base soon observes the following henomenon: almost everything you write down is false. By this we mean that for almost every axiom 1, there exist secial cases when it does not hold. For examle \Cars have four wheels." and \Birds y." are tyically but not universally true statements. As a result, we require some mechanism to allow such statements to be droed or `relaxed' in the face of strong evidence to the contrary. This is articularly the case when we construct novel concets as combinations of old ones: often, tyical roerties of the old concets will no longer make sense for the new comosition. Before discussing this issue further, we note that it diers from the roblem of terminological errors which Guha's context mechanism in CYC sought to address [Blair et al., 1992]. Guha was similarly concerned that when a knowledge engineer wrote bird ) flies it might sometimes be false, but for a dierent reason: Not because only 95% of living birds y, but because the knowledge engineer had failed to state the assumtion that bird meant \living bird" (say). This can be viewed as a terminological error, as the knowledge engineer had written bird when he/she meant living-bird. Guha was concerned that the knowledge engineer hadn't correctly exressed what he/she meant, whereas we are concerned that, even if the engineer did exress what he/she meant as an axiom, it is only true in a robabilistic sense. Guha was concerned with making assumtions exlicit, whereas we are concerned that axioms over-state most common-sense `facts'. 2 Concet Construction as Constraint Relaxation 2.1 An Illustration of The Problem Given many axioms are not universally true (in the world), it may be necessary to ignore or `over-ride' them if substantial evidence contradicts them. This requirement has become articularly aarent in our goal to construct novel concets (such as the RocketBus, described earlier in Working Note 1) through comosition of old concets. Tyically, the new, comosed concet is not simly the union of axioms about its comonents, but also requires droing some of the axioms from the old comonents. 1 (or rule or frame: we consider these terms synonymous in this note.) 1

2 As a toy examle for illustration uroses, consider the comosed concet of a lava kayak, namely a kayak which travels through hot lava rather than water. Our KB may contain the following axioms about kayaks (and related concets): 1. "Kayaks are made of lastic." 2. "Kayaks travel through water." 3. "Seed of a vehicle is / 1 / the viscosity of the medium moved through." 4. "Melt tem of the vehicle's material than tem of the medium moved through." and also: 5. "Water has low temerature and low viscosity." 6. "Plastic has melting temerature." For normal kayaks, alying these axioms we get a concet descrition: kayak(made_of => lastic(melt_tem => lo), seed => hi, travels_thru => water(density => lo,tem => lo)) However, if we ask about a lava kayak ie. we assert 7. "Lava kayaks travel through lava." 8. "Lava has high temerature and high viscosity." then we start to hit contradictions in the KB: Axioms 7 and 2 directly contradict. Axioms 1, 4, 7 and 8 contradict (the lava kayak can't made of lastic, or else it'll melt) 2.2 The Task viewed as Constraint Relaxation In order to roerly describe lava kayak, we need some mechanism to allow axioms to be droed if necessary. A simle algorithm is to try alying each axiom in turn to the new concet, and just ignore it if it causes a contradiction. This leads to the rst descrition of lava kayak shown in Figure 1. However, the resulting descrition is not articularly intuitive (we've retained the kayak being made of lastic, and droed the law of hysics saying it would melt). A more lausible descrition is the second one given in Figure 1, where we dro the axiom that the lava kayak is made of lastic instead. This illustrates that, as well as being able to dro axioms, we need to exress some reference about which axioms to dro. For examle, laws of hysics and denitions should be referrable to kee than axioms stating tyical roerties of concets. 2

3 { A descrition of lava kayak, formed by selecting a consistent subset of axioms: Axiom Ok? 1. "Kayaks are made of lastic." 2. "Kayaks travel through water." 3. "Seed inversely roortional to viscosity." (contradicts 7) 4. "Melting tem of material tem of medium." (contradicts 1) Resulting descrition: lava kayak(made of => lastic(melt tem => lo), seed => lo, travels thru => lava(density => hi,tem => hi) An alternative descrition, formed by selecting a dierent, consistent subset of axioms: Axiom Ok? 1. "Kayaks are made of lastic." (contradicts 4) 2. "Kayaks travel through water." (contradicts 7) 3. "Seed inversely roortional to viscosity." 4. "Melting tem of material tem of medium." Resulting descrition: lava kayak(made of => thing(melt tem => hi), seed => lo, travels thru => lava(density => hi,tem => hi) Figure 1: Alternative ways of relaxing constraints on lava kayak concet. { Generalizing from this examle, we can view concet comosition as a standard constraint relaxation roblem: Given: A KB of axioms (lus some measure of condence associated with each) A secication of a target concet (ie. the denitional roerties of a new concet such as lava kayak(travels thru=>lava) Find: The `most coherent' descrition of the target concet, ie. the best descrition constructable from a subset of axioms in the KB. The most coherent descrition is the one in which all, or (if imossible) as many as ossible, axioms were alied; or, to be more sohisticated, we can weight some axioms more than others. An evaluation function dening coherence which we've been exerimenting with is: enalize a concet for every axiom which could aly but leads to a contradiction (ie. with the axiom formulated an if...then... rule, enalize if the conditions are satised but the conclusions are contradictory). We can assign dierent enalties with dierent axioms (eg. laws and denitions have high enalties, axioms about associated roerties 3

4 have low enalties). The most coherent concet is then the one which accrues a minimum overall enalty. This task can be viewed as constraint relaxation, as the axioms reresent constraints, and the task is to nd the minimal ignoring or `relaxation' of these constraints. 3 Signicance, Imlications and Problems There are two articularly imortant oints to make about concet construction as constraint relaxation as described in the revious Section. 3.1 Decomosable Concets First, we emhasise the imortance of viewing a concet descrition as a comosition of comonents. Rather than writing down a descrition of kayak er se, we described it as the combination of six axioms (Section 2). This comosed descrition rovides us with the `seams' by which we can break u the concet again { we can selectively dro and add axioms into the descrition. As we've described, the ability to break u concets is imortant for automatically formulating new concet descritions. This contrasts with the aroach of trying to override articular slot-values in a descrition { an aroach which is roblematic as the deendencies between slot-values remains hidden. In short: a concet is better thought of as a comosition of axioms/constraints, rather than a collection of values. Axioms, not slots, rovide the roer dimensions of a concet, as axioms roerly isolate and encasulate individual henomena of the world. As in software engineering, this encasulation is essential for concet reuse. 3.2 Searching for General Coherence rather than a Secic Answer Second, forming a `coherent' concet descrition seems an imortant art of questionanswering, and shows u the limitations of standard inference techniques such as backwardchaining. Consider the question: "What material is a lava_kayak made of?" A backward-chaining algorithm will simly answer lastic, as a rule alies (Axiom 1, Section 2), and not realize the contradictions that this answer imlies (eg. the lava kayak will melt). This rather myoic resonse is caused by the algorithm never looking beyond the rst information it hits which could roduce an answer. To roduce a more common-sense answer (eg. \Something which withstands high temeratures.") it seems necessary to go beyond the immediate connes of a secic question and form a coherent `icture' of the concet of interest. In fact, building a coherent icture from initial facts is what most exert systems already do. Mycin's inference engine (for examle) doesn't simly backward chain to nd an answer, but also asks for and elaborates on other information (through the use of its context mechanism). Mycin's reasoning can be seen as searching for a most coherent model of the atient being diagnosed. This view of exert system reasoning { as searching for a coherent, roblem-secic model at run-time rather than \alying rules" { has been eloquently articulated by Clancey [Clancey, 1992]. As he argues, this view underlies almost all roblem-solving, either imlicitly or exlicitly (more often imlicitly, unfortunately). It is hence not surrising that we too need to adot this view for concet construction. 4

5 3.3 Coherence and Belief Revision Our notion of coherence in Section 2.2 is similar, but not quite the same, as coherence theories of belief revision [Rao and Foo, 1989a]. Rao and Foo dene \maximizing coherence" as retaining as many consistent beliefs as ossible during a state change [Rao and Foo, 1989b]; similarly, we are attemting to minimize the (weighted) number of axioms which are not alied to a concet descrition. However, two dierences are also worth noting: First, we have not yet addressed the issue of belief revision; instead, we have only addressed the construction of an initial set of `beliefs' about a new concet. Second, if a rule's alication is inconsistent, we do not retract the rule or its reconditions (as tyically haens in belief revision systems), but instead reject the rule only for the articular instance which led to a contradiction. This can be viewed as a conservative tye of rule modication: f(x)! g(x) becomes f(x) ^ X 6= x i! g(x), given that f(x i ) and :g(x i ) is known. We have not addressed the issue of when to make more signicant changes to the KB, eg. reject a rule in its entirity. 3.4 The Problem of Constraining Inference This, however, itself raises a new issue: how much elaboration of a concet should be erformed, and how can the rocess be controlled? It seems clear that we want to do more than just answer a question (eg. backward chaining), but also less than comletely elaborating every single detail of the concet of interest. One heuristic method might be to use a deth-limit on the concet descrition being constructed. In other words, if we sketch the concet descrition as a concetual grah, then we only aly axioms that aly to nodes within one (say) arc of the concet of interest, as illustrated in Figure 2. Later, a articular question may romt the `focal oint' in the grah to shift from the original concet to some sub-concet of it, at which oint the grah is further elaborated by alying axioms to nodes within the dethbounded roximity of this new focal oint (Figure 3). A second method of limiting the ool of axioms available is to use some context mechanism (as already discussed in Working Note 2). Axioms are groued according to the class of information they rovide information about (eg. satial roerties, hysical roerties, functional roerties) and then only axioms from relevant context(s) are considered. 4 Concluding Remarks To summarize: Considering concets as a suerosition of axioms rovides us the `seams' by which a concet descrition can be ulled aart. Axioms (rather than slots) roerly encasulate individual henomena about the world. Given many axioms are not universally true, concet comosition can be viewed as a constraint relaxation roblem, in which some minimal droing of axioms is searched for in order to roduce the most coherent descrition of a new concet. Forming a coherent concet descrition is an imortant sub-task of question answering (as haens in most exert systems). The issue of controlling elaboration of a concet is still an oen roblem. 5

6 () * / * Nodes within deth D = 1 of the concet of interest force to seed mass etrol_engine fuel engine bus fuel_tank volatile state gasoline contents gas_tank strength material steel Figure 2: Elaboration of nodes u to distance 1 from a concet of interest. () * / * force etrol_engine to seed engine bus mass Nodes within deth D = 1 of a new focal concet in the grah fuel fuel_tank volatile state gasoline contents gas_tank cost form strength material $1.16/g liquid steel comonents {iron,carbon} 300 melt_tem Figure 3: Further elaboration, as the focal oint in the grah changes. 6

7 References [Blair et al., 1992] Blair, P., Guha, R. V., and Pratt, W. (1992). Microtheories: An ontological engineer's guide. Tech Ret CYC , MCC, Austin, TX. [Clancey, 1992] Clancey, W. J. (1992). Model construction oerators. AI, 53(1):1{116. [Rao and Foo, 1989a] Rao, A. S. and Foo, N. Y. (1989a). Formal theories of belief revision. In KR89 (1st Int Conf on Princiles of KR and Reasoning), ages 369{380, CA. Kaufmann. [Rao and Foo, 1989b] Rao, A. S. and Foo, N. Y. (1989b). Minimal change and maximal coherence: A basis for belief revision and reasoning about actions. In IJCAI-89, ages 966{971. 7