Information Density and Semantic Determinacy - Formal vs Natural Language

Narrative

Practitioner literature on this question clusters around a single, sharpening tension: natural-language prompts are being industrialised as specifications faster than anyone can establish how much behavioural variance they actually leave open. ACM Queue's Eight Myths on Software Engineering and GenAI (Butler, Houck, Storey, Lowdermilk, Clarke and Murphy-Hill, 2026) supplies the cleanest measured number in the lane: rewriting a prompt while preserving its meaning changed the generated code in 46 percent of cases and changed correctness outcomes in 28 percent. That is conditional entropy made concrete, not a rhetorical claim about density. Stack Overflow's 2025 Developer Survey corroborates the practitioner experience of this residual uncertainty from the other direction, recording trust in AI code accuracy falling to 29 percent even as adoption rose to 84 percent, with 66 percent of developers citing output that is almost right but not quite as their top frustration.

The industry's institutional response is spec-driven development, an attempt to reintroduce a formal or semi-formal intermediate artefact between the natural-language prompt and the generated code. Thoughtworks' Technology Radar lists spec-driven development as an active technique, tracking tools such as Amazon's Kiro (covered by InfoQ in August 2025) and GitHub's spec-kit, whose own methodology document is explicit that specifications must be precise, complete and unambiguous enough to generate a working system. Thoughtworks' internal Structured-Prompt-Driven Development writeup by Wei Zhang and Jessie Jie Xia treats prompts themselves as version-controlled, reviewable artefacts specifically to constrain non-determinism, an engineering answer to the same problem the theoretical literature frames as underdetermined behaviour conditional on specification.

Two older strands of practitioner argument bound this new activity. Dijkstra's 1978 EWD667 and Brooks' 1986 No Silver Bullet both hold that no notation, however natural, removes the essential difficulty of specifying behaviour precisely, a position TCG's 2019 rebuttal challenges directly. Amazon's 2015 CACM account of adopting TLA+ remains the strongest industrial evidence that formal specification catches defects testing and code review miss, but it is a narrow, opt-in success at one company rather than a general industry pattern, and DORA's 2025 State of AI-assisted Software Development report finds that AI adoption amplifies whatever technical and organisational discipline a team already has rather than substituting for it. Martin Fowler's site, through Birgitta Böckeler's 2025 pieces, reports the same caution from hands-on experimentation: autonomous AI code generation degrades as application complexity rises, and code itself remains the artefact that actually pins down what a system does.

Evidence quality is uneven across the lane. The Hindle et al. naturalness-of-software result is well replicated in its own terms (lower cross-entropy for code than English under comparable n-gram models) but practitioner outlets rarely state the caveat that this measures token predictability, not semantic determinacy, and several sources in this lane implicitly conflate the two. Requirements-ambiguity research from Berry, Kamsties and Paech is older and thinner on recent measurement; the one genuinely quantified study found trained inspectors miss most ambiguity instances even when primed to look for them, a rare case of measured rather than asserted underdetermination. The freshest and best-measured claims in the lane, on prompt-rewrite variance and developer trust erosion, both date from 2025 to 2026 and deserve more weight than the frequently repeated but thinly sourced formal-methods success stories.