Abductive reasoning

About: Abductive reasoning is a research topic. Over the lifetime, 1917 publications have been published within this topic receiving 44645 citations. The topic is also known as: abduction & abductive inference.

The Role of Prior Belief in Reasoning.

Abstract: In this chapter we examine research that uses well-defined laboratory problems requiring hypothetical thinking and reasoning for their solution. By “well-defined” we mean that all information required to solve the problem according to the instructions is explicitly presented. For this reason, psychologists have traditionally regarded any influence of prior knowledge or belief about the problem content or context to be normatively irrelevant to the definition of a correct answer. Consequently, where such beliefs exert an influence this has often been termed a “bias” by the investigators concerned. The effects of prior belief, however, turn out to be so pervasive in these studies that reasoning researchers in the past decade or so have begun radically to reexamine their assumptions about the nature of rational reasoning. This reassessment has been no where more visible than in the study of deductive reasoning, one of the major paradigms in this field. Typical experiments involve presenting participants with the premises of logical arguments and asking them to evaluate a conclusion presented, or draw one of their own (for reviews, see Evans, Newstead, & Byrne, 1993; Manktelow, 1999). The deduction paradigm has its origins in logicism – the belief that logic provides the rational basis for human reasoning (Evans, 2000a). The modern study of deductive reasoning dates from the 1960s, where it was motivated by the writings of psychologists such as Henle (1962) and especially Jean Piaget (Inhelder & Piaget, 1958), who proposed that adult human reasoning was inherently logical.

A connectionist approach for rule-based inference using an improved relaxation method

Abstract: A connectionist mechanism for an inference problem alternative to the usual chaining method is described. The inference problem is within the scope of propositional logic that contains no variables and with some enhanced knowledge representation facilities. The method is an application of mathematical programming where knowledge and data are transformed into constraint equations. In the network, the nodes represent propositions and constraint equations, and the violation of constraints is formulated as an energy function. The inference is realized as a minimization process of the energy function using the relaxation method to search for a truth value distribution that achieves the optimum consistency with the given knowledge and data. A modified relaxation method is proposed to improve the computational inefficiencies associated with the optimization process. The behavior of the method is analyzed through examples of deductive and abductive inference and of inference with unorganized knowledge. >

Hierarchic autoepistemic theories for non-monotonic reasoning: preliminary report

Abstract: Nonmonotonic logics are meant to be a formalization of nonmonotonic reasoning. However, for the most part they fail to embody two of the most important aspects of such reasoning: the explicit computational nature of nonmonotonic inference, and the assignment of preferences among competing inferences. We propose a method of nonmonotonic reasoning in which the notion of inference from specific bodies of evidence plays a fundamental role. The formalization is based on autoepistemic logic, but introduces additional structure, a hierarchy of evidential spaces. The method offers a natural formalization of many different applications of nonmonotonic reasoning, including reasoning about action, speech acts, belief revision, and various situations involving competing defaults.

The Iconic Moment. Towards a Peircean Theory of Diagrammatic Imagination

Abstract: Einstein famously said, “Imagination is more important than knowledge”. But how to study imagination and how to represent and communicate what the content of imagination may be in the context of scientific discovery? In 1908 Peirce stated that deduction consists of “two sub-stages”, logical analysis and mathematical reasoning. Mathematical reasoning is further divisible into “corollarial and theorematic reasoning”, the latter concerning an invention of a new icon, or “imaginary object diagram”, while the former results from “previous logical analyses and mathematically reasoned conclusions”. The iconic moment is clearly stated here, as well as the imaginative character of theorematic reasoning. But translating propositions into a suitable diagrammatic language is also needed: A diagram is for Peirce “a concrete but possibly changing mental image of such a thing as it represents”. “A model”, he held, “may be employed to aid the imagination; but the essential thing to be performed is the act of imagining” (MS 616, 1906). Peirce had observed that the importance of imagination in scientific investigation is in supplying an inquirer, not with any fiction but, in quite stark contrast to what fiction is, with “an inkling of truth”. Since Peirce’s limit notion of truth precludes gaining any direct insight into the truth, in rational inquiry the question of what the truth may be or what it could be needs to be tackled by imagination. This imaginative faculty is aided by diagrams which are iconic in nature. The inquirers who imagine the truth “dream of explanations and laws”. Imagination becomes a crucial part of the method for attaining truth, that is, of the logic of science and scientific inquiry, so much so that Peirce took it that “next after the passion to learn there is no quality so indispensable to the successful prosecution of science as imagination”. In this paper we investigate aspects of scientific reasoning and discovery that seem irreplaceably dependent on a Peircean understanding of imagination, abductive reasoning and diagrammatic representations.

Peirce and the Art of Reasoning.

Abstract: Drawing on Charles Peirce’s descriptions of his correspondence course on the “Art of Reasoning,” I argue that Peirce believed that the study of logic stands at the center of a liberal arts education. However, Peirce’s notion of logic included much more than the traditional accounts of deduction and syllogistic reasoning. He believed that the art of reasoning required a study of both abductive and inductive inference as well the practice of observation and imagination. Employing these other features of logic, his course foreshadowed a number of developments in twentieth century educational theory: the belief that non-traditional students should be educated, the claim that the art of reasoning (or critical reasoning) was important to all theoretical practices, and that the art of reasoning was important to the overall growth of a person. The upshot is that Peirce’s course in the art of reasoning should make us reconsider making logic courses, under Peirce’s broad conception of logic, required courses in high school and higher education.