Non-Standard Reasoning, Revisited
Johan van Benthem

Abstract:
In this article, non-standard 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
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.