Everything else being equal: A modal logic approach to ceteris paribus preferences

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 ≤ given by u ≤ v& v 6≤ u, and we write u < v. We can then lift the preferences between states to preferences between sets of states, or propositions, by defining two modalities, one over ≤ and the other over <. To treat the next two features, we introduce a global existential modality in our language which allows us to express that preferring p to q is tantamount to preferring every p-situation to every q-situation. One could think of