Inductive Learning, Uncertainty and the Acquisition of Causal Models

Inductive Learning, Uncertainty and the Acquisition of Causal Models Manfred Thuring (thuering@gp.tu-berlin.de) Department of Cognitive Psychology, Berlin University of Technology, Franklinstr. 5-7, 10587 Berlin, Germany Uwe Drewitz (drewitz@gp.tu-berlin.de) Department of Cognitive Psychology, Berlin University of Technology, Franklinstr. 5-7, 10587 Berlin, Germany Leon Urbas (leon.urbas@tu-berlin.de) Center of Human-Machine-Systems, Berlin University of Technology, Jebensstr. 1, 10623 Berlin, Germany Abstract Causal models can be regarded as fundamental knowledge bases consisting of rules for generating explanations and predictions. As we all know, such inferences are not free from uncertainty. In an experiment about acquiring causal models by induction, we investigate the impact of the validity of such models on the certainty of inferences. The results indicate that preliminary models are revised in the light of new informa- tion, and that the degree of validity considerably influences the certainty of predictions. Keywords: Mental models; conditional inferences; induction; uncertainty. rules; causal Introduction Causal reasoning is one of the cornerstones of human cognition and seems as fundamental as our concepts of space and time. Explanations and predictions are crucial for everyday thinking as well as for scientific research. They heavily influence our understanding of the world and guide our judgments, decisions and actions in many respects. Well aware of the central role of causality, philosophy and psychology have been exploring the mental mecha- nisms that underlie causal thinking for many years (White, 1990). Examples of research issues are the perception of causal relations, the structure of causal knowledge or the mechanisms of learning and reasoning in causal contexts. In this paper, we address the issue of acquiring causal models by inductive learning. In particular, we investigate how a causal model may gradually evolve from observa- tions and how its structure may influence the content and certainty of predictive inferences. Basic causal models To start with, what do we mean when we say “A causes Z”, as in the statement “smoking causes lung cancer”? Mackie (1974) proposes four possible interpretations: • A is a necessary and sufficient condition for Z. Smoking (A) is the only cause for lung cancer (Z) and always leads to that effect. • A is a necessary but insufficient condition for Z. Only smokers get lung cancer, but some of them do not, because they are lacking the particular genetic predispositions (C) that cause lung cancer in conjunction with smoking. • A is a sufficient but unnecessary condition for Z since other conditions lead to the same effect. Smoking causes lung cancer, but the inhalation of asbestos particles (B) does as well. • A is an insufficient but necessary part of a condition which itself is unnecessary but sufficient for Z (i.e., either A and C or B cause Z). Smoking in conjunction with certain genetic predispositions causes lung cancer or – alternatively - cancer is caused by asbestos particles. Mackie’s taxonomy of causal statements points to four basic knowledge structures constituting the different mea- nings of “A causes Z”. These structures can be regarded as causal models in the sense of Craik (1943) who coined the term “mental model” for domain specific knowledge of pre- dictive and explanatory power. To represent the (in)suffi- ciency and (un)necessity of conditions for an effect, a causal model can be expressed in terms of conditional rules. Based on Mackie’s definition, four types of models can be distinguished. In this paper, we address three of them. Model of Unique Causation (MUC) A is the only cause for Z. Whenever A occurs Z will occur, and whenever A is missing Z will be missing as well. This implies two conditional rules. R MUC1 : A AE Z R MUC2 : -A AE -Z Model of Complex Causation (MCC) A in conjunction with another condition C forms a complex cause that leads to Z. When A and C occur, Z will occur. When either A or C are missing, Z will not appear. This can be represented by three rules. R MCC1 : (A & C) AE Z R MCC2 : -A AE -Z R MCC3 : -C AE -Z Model of Multiple Causation (MMC) A or B cause Z. When A or B are present, Z will occur too. When both A and B are missing, Z will not appear either. Again, three rules express these relationships.