Strategies in Human Nonmonotonic Reasoning

Abstract

Although humans seem adept at drawing nonmonotonic conclusions, the nonmonotonic reasoning systems that researchers develop are complex and do not function with such ease. This paper explores people's reasoning processes in nonmonotonic problems. To avoid the problem of people's conclusions being based on knowledge rather than on some reasoning process, we developed a scenario about life on another planet. Problems were chosen to allow the systematic study of people's understanding of strict and nonstrict rules and their interactions. We found that people had great difficulty reasoning and we identified a number of negative factors influencing their reasoning. We also identified three positive factors which, if used consistently, would yield rational and coherent reasoning-but no subject achieved total consistency. (Another possible positive factor, specificity, was considered but we found no evidence for its use.) It is concluded that nonmonotonic reasoning is hard. When people need to reason in a domain where they have no preconceived ideas, the foundation for their reasoning is neither coherent nor rational. They do not use a nonmonotonic reasoning system that would work regardless of content. Thus, nonmonotonic reasoning systems that researchers develop are expected to do more reasoning than humans actually do! Humans are certainly very quick to jump to conclusions. We are willing to draw at least tentative conclusions and to act on the basis of these, even though we know that with further information we may have to withdraw the conclusions in favor of others. Such reasoning is called nonmonotonic reasoning because the number of conclusions drawn does not necessarily grow as the set of premises grows-we may have to withdraw some conclusions as more information comes in. The work of logicians and mathematicians on nonmonotonic reasoning aims to formalize this reasoning. The hope is that if such reasoning can be formalized, then it could be embedded in an artificial intelligence system, thereby giving it an intelligent flexibility. And more than this, the hope is that formalizing nonmonotonic reasoning will bring all the benefits that formalizing monotonic reasoning has brought. But there are problems. In particular, there are a number of different nonmonotonic systems, all of which are computationally complex. Thus, Gabbay (1994) remarks There are lots of nonmonotonic mechanisms. It is not clear how they fit into a coherent thematic view. I believe, however, that it is possible to present a good framework. It must be possible. After all, these logics are supposed to analyse human practical reasoning. We humans are more or less coherent so there is something there ! (p. v) And, Brachman (1990) says An irony of work on NMR [nonmonotonic reasoning] is that, while the easy adoption and retraction of assumptions is most useful for speeding up natural everyday reasoning, most current NMR proposals drastically compound the already difficult problem of deductive reasoning. We urgently need to determine how NMR can ...

On using human nonmonotonic reasoning to inform artificial systems

“…Hewson and Vogel (1994;Vogel, 1996) found that most people were reluctant to come to any conclusion for the problems they gave. Ford and Billington (2000) showed that when conclusions could not be retrieved from background knowledge, subjects did not overwhelmingly give the expected answers based on the specificity principle. Thus, for example, in two different studies, only 7 out of 19 and 2 out of 12 subjects drawn from a student population gave the expected, negative, answer to problems with the structure of (1).…”

“…Thus, for example, given all echidnas are mammals, mammals usually do not lay eggs, Susie is an echidna, we can assume (erroneously in fact) that echidnas do not lay eggs and that Susie does not lay eggs, until we hear otherwise. Ford and Billington (2000) gave 19 university students a series of problems like (3) and (4) (though without the diagrammatic representations) where the content was about fictitious plants and animals and where conclusions could therefore not be simply retrieved from memory. For (3), all 19 subjects concluded that Garffi was likely to be found in deserts; for (4), 17 concluded Stordy was likely to be found on cliffs.…”

“…These subjects are thus willing on these simple problems to draw conclusions that the literature on nonmonotonic logic would expect. For problems involving conflicting arguments, people fare less well (Hewson & Vogel, 1994;Vogel, 1996;Ford & Billington, 2000;Ford, in press). Hewson and Vogel (1994;Vogel, 1996) found that most people were reluctant to come to any conclusion for the problems they gave.…”

“…N2 suggests a misunderstanding of an argument. Consider (5), which gives the structure of a problem studied by Ford and Billington (2000). (5) Claiming, as a number of subjects did, that the individual i who is a B was probably a D because there are two positive paths from B to D is simply wrong; there is only one positive path from B to D.…”

Towards a mental probability logic

“…Compared with the long tradition of psychological experiments on classical logics and syllogistics (Rips, 2002(Rips, , 1994JohnsonLaird, 1999;Johnson-Laird & Byrne, 1994;Bacon et al, 2003;Newstead, 2003;Morley et al, 2004), only a few studies, though, have investigated nonmonotonic reasoning empirically (Benferhat et al, in press;Da Silva Neves et al, 2002;Ford & Billington, 2000;Ford, in press, 2004Ford, in press, , 2005Pfeifer, 2002;Pfeifer & Kleiter, 2003, in press;Pelletier & Elio, 2003;Schurz, in press). …”