Everything else being equal: A modal logic approach to ceteris paribus preferences
Johan van Benthem, Olivier Roy, Patrick Girard · 2007
The notion of “preference ” has circulated in many disciplines in the first half of the 20th century, especially in economics and social choice theory (cf. [34]). In logic, Halldén [9] initiated a field of research that was quickly championed by G. H. von Wright in [33], a book that is usually taken to be the seminal work in preference logic. The present paper presents a modal logic for the formalization of preferences as initiated by von Wright. Beside historical concerns, a logic of preference finds an independent modern interest in various (sub-)disciplines of economics, social choice theory, computer science and philosophy, to name a few. For instance, it proved indispensable to investigate the logic of solution concepts of game theory such as backward induction and Nash equilibrium (see [30]). Our preference logic can define a strict global binary relation between propositions which has an essential ceteris paribus rider. We achieve the first features with what we call the basic preference language. We start with a reflexive and transitive accessibility relation ≤ over states, where accessible states are those that are at least as good as the present one. To reason about strict preferences, we take the strict subrelation of ≤