onderscheidingslogica

Onderscheidingslogica is a term used in Dutch-language logic literature to denote the study of how logical systems distinguish between objects, states, or structures. It focuses on what needs to be expressed in a formal language to tell apart elements of a domain and on how different logics compare in their ability to differentiate.

Core ideas in onderscheidingslogica include definability, the question of which properties or predicates can single out a given element, and indistinguishability relations, which capture when two elements cannot be distinguished by formulas of a particular logic. Related concepts are automorphisms and symmetries of structures, and in many areas modal logic, bisimulation serves as a standard tool for analyzing indistinguishability of states. Ehrenfeucht–Fraïssé games are often used to illustrate and quantify the distinguishing power of first-order logic between structures.

A central aim is to compare logics by their distinguishing power: for two structures A and B, does a sentence in a given logic differentiate them? If not, A and B are considered indistinguishable within that logic’s expressive scope, often described as elementary equivalence with respect to that logic.

Onderscheidingslogica intersects philosophy, computer science, and linguistics. It informs topics such as program equivalence, model checking, knowledge representation, and database theory by examining how expressive a language must be to distinguish between different models, states, or data items.