The Logic of Resources and Capabilities

TL;DR

The paper introduces LRC, a logic that combines abilities and resource reasoning to model social behavior in organizations, supported by formal properties and case studies.

Contribution

It presents a novel logic LRC unifying agency and resource logics, with formal proofs and extensions for modeling organizational issues.

Findings

LRC is sound, complete, and has desirable proof-theoretic properties.

Case studies demonstrate LRC's applicability to planning and organizational theories.

Framework extensions retain core properties while modeling complex scenarios.

Abstract

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, 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 multi-type 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.