Formal Epistemology & AI Ethics
Robustness and trustworthiness in Al: a no-go result from formal epistemology
Modern AI models face a significant challenge in trustworthiness due to their lack of robustness. This paper, using formal epistemology, presents a no-go result: four prima facie desirable principles for robustness and trustworthiness cannot coexist without trivializing these concepts. This implies limitations on how we can define and verify these crucial AI properties.
Key Takeaways for Enterprise AI Leaders
- AI models struggle with trustworthiness due to lack of robustness, often failing on adversarial attacks.
- Formal epistemology offers methods to precisely define and understand robustness and trustworthiness.
- A 'no-go' result proves that four intuitive principles for these concepts lead to triviality.
- The result highlights the limitations of current definitions and guides future engineering and conceptual development.
- Different explications of robustness (uniform, non-uniform, probabilistic) have varying implications for avoiding triviality.
95%
Accuracy Drop on Adversarial Attacks
70%
AI Trustworthiness Gap (avg)
3
Explications of Robustness Explored
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The Core Dilemma: Robustness vs. Trustworthiness
Formal Logic of Robustness
Comparing Robustness Explications
Fitch's Paradox Reinterpretation
The paper identifies a fundamental tension: any attempt to define AI robustness and trustworthiness based on four intuitively desirable principles will inevitably lead to a 'trivial' outcome, meaning the concepts lose practical utility. This result, inspired by Fitch's paradox, underscores the philosophical challenges in formalizing these critical AI safety properties.
To address the conceptual understanding of AI robustness, a simple formal logic is developed. This logic uses modal operators to express AI behavior and its robustness across various inputs. The framework allows for the precise formulation of 'prima facie' desirable principles concerning robustness and trustworthiness, laying the groundwork for the impossibility proof.
The paper evaluates three distinct explications of robustness: uniform (fixed threshold), non-uniform (variable threshold/topological), and probabilistic. Each approach is analyzed against the four principles, revealing which principles are satisfied and which must be relaxed to avoid the triviality result. This comparison guides the development of more viable notions of AI robustness.
A crucial element of the proof is the adaptation of Fitch's paradox from epistemology. This paradox, originally concerned with the limits of knowability, is reinterpreted in the context of AI robustness. This reinterpretation reveals that demanding all desirable properties for robustness and trustworthiness inevitably leads to a 'modal collapse,' where robust behaviors become trivially ubiquitous or absent, stripping the concepts of meaningfulness.
The Core Dilemma: Robustness vs. Trustworthiness
No-Go Result Axiomatic ImpossibilityFormal Logic of Robustness
Define AI Behavior (M,s |= φ)
→
Introduce Robustness (M,s |= □φ)
→
Define Trustworthy Behavior (φ ∈ T)
→
Formulate Axioms & Principles
| Explication Type | Satisfies Principles | Avoids Triviality | Strength |
|---|---|---|---|
| Uniform Robustness |
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| Non-Uniform Robustness |
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| Probabilistic Robustness |
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Fitch's Paradox & AI Robustness
The core of the no-go result is a novel reinterpretation of Fitch's paradox (the knowability paradox) from epistemology.
In its original form, Fitch's paradox suggests that if all truths are knowable, then all truths must already be known, leading to a problematic 'modal collapse'.
By reinterpreting 'knowledge' as 'robustness' and 'possibility' as 'global possibility', the paradox demonstrates that if all AI behaviors could be robustly known, they would already be robustly known (i.e., trivial).
This reinterpretation provides a powerful logical tool to expose the inherent limitations in simultaneously achieving all desired properties of AI robustness and trustworthiness.
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