# Counting Worlds Branching Time Semantics for post-hoc Bias Mitigation in generative AI

arXiv: https://arxiv.org/abs/2604.19431 · HTML: https://mlsanity.com/paper/2604.19431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [Bias in Large Language Models: Origin, Evaluation, and Mitigation](https://mlsanity.com/paper/2411.10915/) (2024)
- [Investigating Bias in LLM-Based Bias Detection: Disparities between LLMs and Human Perception](https://mlsanity.com/paper/2403.14896/) (2024)
- [Current state of LLM Risks and AI Guardrails](https://mlsanity.com/paper/2406.12934/) (2024)
- [Quantifying Societal Bias Amplification in Image Captioning](https://mlsanity.com/paper/2203.15395/) (2022)
- [UniBias: Unveiling and Mitigating LLM Bias through Internal Attention and FFN Manipulation](https://mlsanity.com/paper/2405.20612/) (2024)
- [Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination](https://mlsanity.com/paper/1709.02093/) (2017)
- [Bridging the Safety Gap: A Guardrail Pipeline for Trustworthy LLM Inferences](https://mlsanity.com/paper/2502.08142/) (2025)
- [BiasFilter: An Inference-Time Debiasing Framework for Large Language Models](https://mlsanity.com/paper/2505.23829/) (2025)
- [Simulating a Bias Mitigation Scenario in Large Language Models](https://mlsanity.com/paper/2509.14438/) (2025)
- [Checking Trustworthiness of Probabilistic Computations in a Typed Natural Deduction System](https://mlsanity.com/paper/2206.12934/) (2022)
- [DSO: Direct Steering Optimization for Bias Mitigation](https://mlsanity.com/paper/2512.15926/) (2025)
- [On Counting Propositional Logic](https://mlsanity.com/paper/2103.12862/) (2021)
- [Formal Verification of Markov Processes with Learned Parameters](https://mlsanity.com/paper/2501.15767/) (2025)
- [Trustworthiness Preservation by Copies of Machine Learning Systems](https://mlsanity.com/paper/2506.05203/) (2025)
- [A Linear Temporal Logic of Frequencies on Series of Events](https://mlsanity.com/paper/2604.10669/) (2026)

## Abstract (arXiv)

Generative AI systems are known to amplify biases present in their training data. While several inference-time mitigation strategies have been proposed, they remain largely empirical and lack formal guarantees. In this paper we introduce CTLF, a branching-time logic designed to reason about bias in series of generative AI outputs. CTLF adopts a counting worlds semantics where each world represents a possible output at a given step in the generation process and introduces modal operators that allow us to verify whether the current output series respects an intended probability distribution over a protected attribute, to predict the likelihood of remaining within acceptable bounds as new outputs are generated, and to determine how many outputs are needed to remove in order to restore fairness. We illustrate the framework on a toy example of biased image generation, showing how CTLF formulas can express concrete fairness properties at different points in the output series.