Nonstandard Reasoning

In this article, nonstandard reasoning refers to the proliferation of reasoning styles investigated in modern logic beyond its traditional agenda. After a brief statement of standard logical approaches to consequence, we describe motivations for new systems. These include not only inference patterns with special vocabulary from mathematics, philosophy, and linguistics but also new styles of reasoning coming from computer science and artificial intelligence. The resulting landscape is diverse, but we discuss unifying themes such as structural rules, preferences, resources, information, and architecture of logical systems. Many of these reflect recent cognitive trends in modern logic putting ‘social dynamics’ at center stage: reasoning about one’s own information and that of others, information update, acts of communication, processes of inquiry, and games.