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THE LOGIC OF RESOURCES AND CAPABILITIES

  • MARTA BÍLKOVÁ (a1), GIUSEPPE GRECO (a2), ALESSANDRA PALMIGIANO (a3), APOSTOLOS TZIMOULIS (a4) and NACHOEM WIJNBERG (a5)...
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, 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.

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Corresponding author
*DEPARTMENT OF LOGIC, FACULTY OF ARTS CHARLES UNIVERSITY PRAGUE, CZECH REPUBLIC E-mail: marta.bilkova@ff.cuni.cz
DEPARTMENT OF LANGUAGES, LITERATURE AND COMMUNICATION UNIVERSITY OF UTRECHT UTRECHT, THE NETHERLANDS E-mail: G.Greco@uu.nl
FACULTY OF TECHNOLOGY, POLICY AND MANAGEMENT DELFT UNIVERSITY OF TECHNOLOGY DELFT, THE NETHERLANDS and DEPARTMENT OF PURE AND APPLIED MATHEMATICS UNIVERSITY OF JOHANNESBURG JOHANNESBURG, SOUTH AFRICA E-mail: A.Palmigiano@tudelft.nl
§FACULTY OF TECHNOLOGY, POLICY AND MANAGEMENT DELFT UNIVERSITY OF TECHNOLOGY DELFT, THE NETHERLANDS E-mail: A.Tzimoulis-1@tudelft.nl
**FACULTY OF ECONOMICS AND BUSINESS UNIVERSITY OF AMSTERDAM AMSTERDAM, THE NETHERLANDS and COLLEGE OF BUSINESS AND ECONOMICS UNIVERSITY OF JOHANNESBURG JOHANNESBURG, SOUTH AFRICA E-mail: N.M.Wijnberg@uva.nl
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