Kamp's theorem, proved by Hans Kamp in his 1968 doctoral thesis Tense Logic and the Theory of Linear Order, states that linear temporal logic is exactly as expressive as monadic first-order logic of order over the non-negative integers and over the real numbers, making it the oldest result in the study of expressive completeness for temporal logics. In the thesis, Kamp introduced the until and since operators to Arthur Prior's tense logic and showed that the earlier X, Y, F and P operators alone cannot express the until operator, so the added operators were needed to reach full expressive completeness.
Facts
StatementLinear temporal logic is equivalent to the monadic first-order logic of order over the non-negative integers and the real numbers. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Kamp's theorem (Wikipedia)
Sources
1. Kamp's theorem (Wikipedia)
Introduction
linear temporal logic is equivalent to the monadic first-order logic of order over the non-negative integers and the real numbers
Introduction [proof-year]
The theorem was proven by Hans Kamp in his doctoral thesis, Tense Logic and the Theory of Linear Order (1968)
In Branch: Logic and Foundations, Lead sentence
In mathematical logic and computer science, Kamp's theorem states that linear temporal logic is equivalent to the monadic first-or
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.