Flexibility in Ceteris Paribus Reasoning

Abstract

Ceteris Paribus clauses in reasoning are used to allow for defeaters of norms, rules or laws, such as in von Wright’s [The Logic of Preference, 1963] example “I prefer my raincoat over my umbrella, everything else being equal”. In [Girard 2008, van Benthem, Girard, and Roy 2008], a logical analysis is offered in which sets of formulas Γ, embedded in modal operators, provide necessary and sufficient conditions for things to be equal in ceteris paribus clauses. For most laws, the set of things allowed to vary is small, often finite, and so Γ is typically infinite. Yet the axiomatisation they provide is restricted to the special and atypical case in which Γ is finite. We address this problem by being more flexible about ceteris paribus conditions, in two ways. The first is to offer an alternative, slightly more general semantics, in which the set of formulas are only give necessary but not (necessarily) sufficient conditions. This permits a simple axiomatisation. The second is to consider those sets of formulas which are sufficiently flexible to allow the construction of a satisfying model in which the stronger necessary-and-sufficient interpretation of [3, 4] is maintained.