FRANCIS JEFFRY PELLETIER and RENÉE ELIO THE CASE FOR PSYCHOLOGISM IN DEFAULT AND INHERITANCE REASONING

Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to argumentation in which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning. The informal notion has been seen as central to a number of areas of scholarly investigation, and we canvass some of them before turning our attention to its role in AI. It is because ordinary people so cleverly and effortlessly use default reasoning to solve interesting cognitive tasks that nonmonotonic formalisms were introduced into AI, and we argue that this is a form of psychologism, despite the fact that it is not usually recognized as such in AI. We close by mentioning some of the results from our empirical investigations that we believe should be incorporated into nonmonotonic formalisms. 1. DEFAULT AND NONMONOTONIC REASONING Default reasoning occurs whenever the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn; that is, does not deductively force the reasoner to draw the conclusion under consideration. (‘Force’ in the sense of being required to do it if the reasoner is to be logically correct). But nonetheless the reasoner does draw the conclusion. For example, from the statements ‘Linguists typically speak more than three languages’ and ‘Kim is a linguist’, one might draw the conclusion, by default, ‘Kim speaks more than three languages’. What is meant by Synthese (2005) 146: 7–35 © Springer 2005 8 FRANCIS JEFFRY PELLETIER AND RENÉE ELIO the phrase ‘by default’ is that we are justified in making this inference because we have no information which would make us doubt that Kim was covered by the generalization concerning linguists or would make us think that Kim was an abnormal linguist in this regard. Of course, the inference is not deductively valid: it is possible that the premises could be true and the conclusion false. So, one is not forced to draw this conclusion in order to be logically correct. Rather, it is the type of conclusion that we draw “by default” – the type of conclusion we draw in the ordinary world and ordinary circumstances in which we find ourselves. The example just given perhaps makes it seem obvious that default reasoning occurs in certain circumstances, namely those in which we are given explicit statements of typicality or normality or usualness or “for the most part” (‘Linguists typically/normally/usually/mostly speak more than three languages’). But not only do these explicit statements of typicality involve default reasoning, but so too do some ordinary statements without any restrictions. For example, such statements as ‘Birds fly’, ‘Cigarette smoking causes cancer’, ‘Ravens are black’, ‘Mary smokes a cigarette after dinner’, ‘Frenchmen eat horsemeat’, ‘Telephone books are thick’, and many others, are said to be statements involving default reasoning in that they tolerate exceptions. (A statement “tolerates exceptions” if it is true despite the existence of instances that the predicate of the statement does not truly characterize: non-flying birds, thin telephone books, instances of non-after-dinner-cigarette-smoking behavior by Mary). It has been argued (Schubert and Pelletier 1987) that there is no upper number or percentage of exceptions which these statements can allow and still be true. An alternative explanation might be that such statements are “strictly speaking” or “literally" false, but we somehow understand and use them as if they had an explicit ‘usually’ or ‘typically’, etc. We will not here consider this alternative explanation – it has not garnered a very favorable reception in the literature with which we are here concerned. It makes even the classic “Snow is white” be literally false! (For further discussion, see Krifka et al. 1995). Formally speaking, the term ‘non-monotonic reasoning’ refers to argumentation in which one uses certain information (the premises of the argument) to reach a conclusion, but where it is possible that later adding some further information to those very same premises (i.e., adding another premise to the existing premises of the argument) could make one want to retract the original conclusion. (Sometimes this might even make us wish to conclude the opposite of the original conclusion.) Importantly, this retraction of the original conclusion is not accompanied by a desire to retract any of the original premises. It is this retractionTHE CASE FOR PSYCHOLOGISM IN DEFAULT AND INHERITANCE REASONING 9 of-conclusion-without-concomitant-desire-to-retract-a-premise which sets non-monotonic reasoning apart from classical monotonic reasoning. Put symbolically, it is a case of non-monotonic reasoning if one is willing to make the inference {P1, P2, . . . Pn} ∴ C but is unwilling to make the inference {P1, P2, . . . Pn, Pn+1} ∴ C. The catch-phrase that is the hallmark of non-monotonic reasoning is “that new information makes one withdraw previously-made inferences”.1 It is easily seen that the informal notion of default reasoning manifests a type of non-monotonic reasoning. In the above example, for instance, we concluded that Kim spoke at least three languages. But were we to add to our list of premises the further fact that Kim graduated from NewWave University, which we know has revoked all language requirements, we then would wish to withdraw the earlier conclusion. Thus, default reasoning is a species of non-monotonic reasoning. More generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged possible existence of “exceptional instances” of the class. In the absence of explicit information that any particular object is one of the “exceptional instances”, we are enjoined to apply the default statement to the object. However, further information may arrive telling us that this object in fact is one of the “exceptional” ones. This is where non-monotonicity resides in default reasoning. Various philosophers and logicians have tried to give an account of how ordinary people perform default reasoning. In general, the view taken by most of these earlier philosophers was that the people in question “jumped to conclusions” which were not really logically justifiable, but which were required to be made on the basis of insufficient information.2 A natural outgrowth of this attitude toward people’s use of non-monotonic reasoning is that such reasoning “really” is bad deductive reasoning – perhaps justifiable on the grounds of having to “get on with it” in the face of limited resources such as time and energy, but bad nonetheless. This attitude is quite common in the philosophical literature on defeasible reasoning. A similar attitude toward probabilistic reasoning is also quite common in some of the psychological literature. For example, Tversky and Kahneman (1983) found that people will assign a lower probability to the proposition There will be a very severe earthquake in costal California in the next three years than they do to the proposition There will be a very severe earthquake in costal California in the next three years and property damage will exceed $500 million because numerous houses will fall into the ocean. Yet of course the second proposition is a conjunction with the first proposition as one of its conjuncts, and therefore the second proposition cannot have a higher probability than the first. Tversky and Kahneman view people as 10 FRANCIS JEFFRY PELLETIER AND RENÉE ELIO ignoring relevant information and making mistakes in their probabilistic reasoning. But non-monotonic reasoning, in our view, is not an example of bad deductive reasoning. It is not an example of doing something wrong. Following many theoreticians in artificial intelligence (AI), we believe that it is correct to make such inferences. It is not a mistake on people’s part, nor is it a matter of “having to do something, anything, in the face of insufficient information”. Rather, it is right and proper to make such inferences: not only is this what people in fact do, but it is what people (and artificial agents) ought to do. 2. USES OF DEFAULT REASONING As remarked above, many logicians question whether the notion of nonmonotonic logic is coherent. But interesting as this question is, we do not propose to investigate the philosophical question of whether nonmonotonic logic makes any “deep” sense. Instead we lay out a number of academic realms that have employed default reasoning, with an eye to demonstrating just how widespread the phenomenon really is. We think that the independent appearance of this mode of reasoning in widelydivergent fields, with little evidence of any cross-fertilization, shows how pervasive it is and how deeply this sort of reasoning seems to be embedded in our explanations of nature and of human nature. We find it rather surprising that there has been so little cross-fertilization amongst these different areas, and would urge researchers to seek out the investigations carried out in fields other than their own. Here we only mention, rather than characterize fully, certain areas in which the notion of default reasoning has been investigated.