Towards a logic of affordances
Rafal Gruszczynski, Paula Menchón, Ivo Düntsch, Günther Gediga
TL;DR
The paper grounds a formal theory of affordances in Gibson's action-possibility concept by modeling them as ternary relations among actors, objects, and environments. It builds a framework on Pawlak information systems and rough sets to define both crisp and rough (approximate) affordances, and develops modal-style operators (possibility and sufficiency) together with upper/lower approximation operators for triadic contexts. Through concrete examples (pets, toys, dog parks, and playgrounds) and rigorous definitions, the work shows how granularity and equivalence classes shape reasoning about what actions are possible or inevitable in given environments. The study lays groundwork for a future multi-sorted, mixed-logic formalism that integrates information-system properties, enabling systematic deduction of actions, concepts, and their ecological constraints.
Abstract
We aim to construct a formal theory of affordances seen as ternary relations. Beginning with a characterization of affordances proposed by James J. Gibson, and utilizing the tools provided by Zdzisław Pawlak's information systems and rough sets, we construct a mathematically precise definition of both crisp and rough affordances. Then, we analyze modal and approximation operators that enable reasoning about affordances in both scenarios.