A special issue on structural proof theory, automated reasoning and computation in celebration of Dale Miller’s 60th birthday

The genesis of this special issue was in a meeting that took place at Université Paris Diderot on December 15 and 16, 2016. Dale Miller, Professor at École polytechnique, had turned 60 a few days earlier. In a career spanning over three decades and in work conducted in collaboration with several students and colleagues, Dale had had a significant influence in an area that can be described as structural proof theory and its application to computation and reasoning. In recognition of this fact, several of his collaborators thought it appropriate to celebrate the occasion by organizing a symposium on topics broadly connected to his areas of interest and achievements. The meeting was a success in several senses: it was attended by over 35 people, there were 15 technical presentations describing new results, and, quite gratifyingly, we managed to spring the event as a complete surprise to Dale.

THE LOGIC OF RESOURCES AND CAPABILITIES

We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC (soundness, completeness, canonicity, and disjunction property) and its associated analytic calculus (conservativity, cut elimination, and subformula property). These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations.