Reply to Seligman

A Seligman-Style Tableau System

Proof systems for hybrid logic typically use @-operators to access information hidden behind modalities; this labeling approach lies at the heart of most resolution, natural deduction, and tableau systems for hybrid logic. But there is another, less well-known approach, which we have come to believe is conceptually clearer. We call this Seligman-style inference, as it was first introduced and e...

From Helplessness to Hope: The Seminal Career of Martin Seligman

This book explores a specific field of psychological research, but it also celebrates the profound contributions to this field of Martin E. P. Seligman. Therefore, the book blends the history of this research enterprise and Seligman's own intellectual history. This chapter reviews the modest origins of the phenomenon of "learned helplessness" in the animal laboratory, its extensions to human be...

The Authors’ Reply

The Authors’ Reply

Synthetic completeness proofs for Seligman-style tableau systems

Hybrid logic is a form of modal logic which allows reference to worlds. We can think of it as ‘modal logic with labelling built into the object language’ and various forms of labelled deduction have played a central role in its proof theory. Jerry Seligman’s work [13,14] in which ‘rules involving labels’ are rejected in favour of ‘rules for all’ is an interesting exception to this. Seligman’s a...