Automating Human Inference

1 Abstract Researchers of reasoning in computer science and psychology are estranged sib-lings. The tools they use to investigate patterns of inference seldom overlap, because the goals of each group differ. A computer scientist's primary goal is to efficiently engineer systems based on logical calculi. But, human reasoning systematically violates the constraints imposed by orthodox logic. One logician described the disparity between logical systems and the everyday inferences they are intended to capture as " one of the greatest scandals of human existence " [1]. And so the psychological objective is to discover patterns of reasoning in humans, both normative and fallacious, with the ultimate goal of developing theories capable of predicting human inference. Despite their diverging purposes, computer scientists and psychologists face similar theoretical challenges: how is knowledge represented and integrated into reasoning processes? What constitutes a normative inference? Why are some inferences more difficult than others? Human reasoning is predictably irrational, but it can also be more productive, flexible, and capable than current automated reasoning systems. Indeed, as some researchers argue, certain kinds of inference – such as reasoning about defaults, non-monotonic inference, explanatory reasoning , and conditional inference – cannot be characterized without reference to how humans make them [14, 16]. A keen understanding of human reasoning therefore has both psychological and computational value. Present day automated reasoning systems do not reason the way humans do – which may explain their success as inferential tools. The productivity of automated theorem provers (ATPs) has advanced by orders of magnitude since McCune's famous solution to the Robbins problem [13]. ATPs regularly compete against one another at international competitions to efficiently yield proofs of thousands of reasoning problems. For instance, the ATPs that entered the 2004 theorem-proving competition at the annual Conference on Automated Deduction (CADE) [18] were designed to solve two thousand eligible problems. At the same competition ten years later, the number of eligible problems grew to fifteen thousand [17]. As a result of prolonged development, ATPs now routinely serve as productive analytical tools, and they are instrumental in diverse applications , such as the verification of transportation systems, electrical circuitry, and automation systems. But, ATPs are designed to carry out just one inferential task, i.e., they operate by deriving a valid proof of a conclusion from a given set of premises. This design constraint allows systems to filter out invalid inferences that may corrupt further processing, but …