Temporallogikk

Temporallogikk, or temporal logic, is a formal framework for reasoning about propositions through time. It extends classical logic with operators that refer to temporal relations, allowing statements about how truth values change as time progresses. In computer science, temporallogikk is used to specify and verify the behavior of dynamic systems, such as concurrent processes and real-time software.

The theory distinguishes between linear-time logics, which consider a single timeline of moments, and branching-time logics, which allow many possible futures from a given moment. Semantics are typically given by temporal models or Kripke structures: a sequence of time points, a valuation of propositional variables at each point, and a relation that defines how moments are connected. Truth conditions specify how formulas hold along those timelines.

Core operators include X (next), F (eventually), G (globally/always), and U (until). Past-oriented variants provide operators such as P (previous) and H (historically). Major families include Linear Temporal Logic (LTL), Computation Tree Logic (CTL), and the more expressive CTL*, each with different ways of quantifying over paths in a model.

Applications are central in formal verification and model checking, particularly for hardware and software systems, to prove properties like safety and liveness. Temporal logic is also used in specification languages such as TLA+ and in theoretical foundations of verification methodologies. A common example: G (request → F acknowledge) expresses that every request is eventually acknowledged.