Übergangslogik

Übergangslogik is a branch of mathematical logic and theoretical computer science that studies the logical principles governing state changes in dynamical systems and computational processes. Its central aim is to provide formal languages and semantics to describe how a system evolves from one state to another through transitions. A typical framework uses a transition system T = (S, →, L) where S is a set of states, → ⊆ S×S is a transition relation and L assigns truth values to atomic propositions at each state. Formulas are interpreted over states and, in many variants, over runs, so that one can reason about how truth values evolve along executions.

In practice, transitions are often enriched with labels or actions, leading to labeled transition systems. Temporal or modal operators—such as next, eventually, and always—are used to express properties about future states along computations. The field covers a range of logics from basic modal logic to richer temporal logics that combine state-based reasoning with path-based properties and notions such as bisimulation, model checking, and verification.

Übergangslogik is closely related to automata theory, formal verification, and model checking, where the goal is to automatically determine whether a system satisfies a given specification. It also connects to control theory and, in some contexts, to linguistics and philosophy, where ideas about system dynamics and process semantics are relevant.

Historically, it builds on modal and temporal logics and has evolved with developments in automated verification and specification languages. Its tools and concepts provide a formal foundation for analyzing and reasoning about dynamic behavior across various domains.