# Axiomatic systems and topological semantics for intuitionistic temporal logic

arXiv: https://arxiv.org/abs/1803.05077 · HTML: https://mlsanity.com/paper/1803.05077/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Applications of Intuitionistic Temporal Logic to Temporal Answer Set Programming](https://mlsanity.com/paper/2603.14692/) (2026)

## Abstract (arXiv)

We propose four axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. Our topological semantics features a new interpretation for the `henceforth' modality that is a natural intuitionistic variant of the classical one. Using the soundness results, we show that the four logics obtained from the axiomatic systems are distinct. Finally, we show that when the language is restricted to the `henceforth'-free fragment, the set of valid formulas for the relational and topological semantics coincide.