This book is a philosophical interpretation of relevant logic. Relevant logic, also called ‘relevance logic’, has been around for at least half a century. It has been extensively developed and studied in terms of its mathematical properties. So relevant logic is a highly developed and mathematically well-understood branch of non-classical logic. But what is it good for and why should we adopt it? I think that it is a good tool for understanding ordinary deductive reasoning and that it provides us with the tools to understand conditionals. And that is what this book is all about.

Unlike intuitionist logic, relevant logic does not come packaged with its own philosophy. There are intuitionists, and they all share a large number of important philosophical views that non-intuitionists reject. Although some relevant logicians have talked about ‘the relevantist’, relevantism is not a well-developed view, nor one that is widely held even by relevant logicians. By and large, we are free to adopt their own philosophical interpretation of relevant logic.

Historically, my own view developed out of my acquaintance with the possible worlds approach to semantics. When I was a graduate student, I studied modal logic and Montague grammar and found the framework of possible worlds to be a very intuitive, elegant and powerful framework in which to do semantics. Later, after I had become immersed in relevant logic, I wanted to give others the same sort of feeling of being at home in relevant logic that I had felt when I was first exposed to possible world semantics. This book is the latest product of that attempt.

I begin with the possible worlds framework.