Toward a Logic of Everyday Reasoning

Logic should return its focus to valid reasoning in real-world situations. Since classical logic only covers valid reasoning in a highly idealized situation, there is a demand for a new logic for everyday reasoning that is based on more realistic assumptions, while still keeps the general, formal, and normative nature of logic. NAL (Non-Axiomatic Logic) is built for this purpose, which is based on the assumption that the reasoner has insufficient knowledge and resources with respect to the reasoning tasks to be carried out. In this situation, the notion of validity has to be re-established, and the grammar rules and inference rules of the logic need to be designed accordingly. Consequently, NAL has features very different from classical logic and other non-classical logics, and it provides a coherent solution to many problems in logic, artificial intelligence, and cognitive science. Keyword: non-classical logic, uncertainty, openness, relevance, validity 1 Logic and Everyday Reasoning 1.1 The historical changes of logic In a broad sense, the study of logic is concerned with the principles and forms of valid reasoning, inference, and argument in various situations. The first dominating paradigm in logic is Aristotle’s Syllogistic [Aristotle, 1882], now usually referred to as traditional logic. This study was carried by philosophers and logicians including Descartes, Locke, Leibniz, Kant, Boole, Peirce, Mill, and many others [Bocheński, 1970, Haack, 1978, Kneale and Kneale, 1962]. In this tradition, the focus of the study is to identify and to specify the forms of valid reasoning Pei Wang Department of Computer and Information Sciences, Temple University, Philadelphia, USA e-mail: [email protected]