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Kamp's Theorem

Logic and Foundations

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
Statement
Linear temporal logic is equivalent to the monadic first-order logic of order over the non-negative integers and the real numbers. 1
Proof Year
1968 1
Classification
Statement Form
Characterization 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
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