# Logical English

**In short:** Logical English lets lawyers write executable norms as
controlled English sentences; Arxo writes them as rules with declared
priorities and judgment channels. This page — one of three separate
Prolog-family studies alongside PROLEG and Blawx — is for readers who
author norms in near-natural language and want the exact semantic seams:
negation, burden, goal order, and completion.

## What Logical English is for

Logical English is a controlled natural-language surface over logic
programming: norms read as sentences with templates as the explicit
surface contract. Its strengths are lawyer-readable authoring with
mathematical precision, honest openness (unknowns and judged questions
left to a human or a scene instead of invented), expectations written as
tests next to the rules, and explanations in the words of the source
sentences with provenance quotes and quote checks. Exceptions use a
disciplined unless-form — with version caveats below.

## Where it meets Arxo

Controlled language as the recording surface for norms and explanations is
the shared intersection. The studied scenario models one citizenship
article as enacted, in a tiny public model on one side and a new Arxo
mini-package on the other, comparing answer signs, grounds, and
open-question handling across twelve cases plus four edits (territory
readings, a commencement date, registration, a foundling presumption).

## Key differences

- **Negation is failure to prove.** "It is not the case that" means the
  goal could not be established; there is no built-in strong negation —
  opposites are separate explicit predicates. "Not proven" and "proven
  not" must never be conflated; Arxo keeps them as distinct answers with
  distinct producers.
- **Burden names no authority.** A judged question carries no organ; open
  and evaluative questions become scene facts or assumptions. Arxo routes
  them through a typed judgment request to a named organ with an
  observable requires-judgment outcome.
- **Goal order and completion are layout and engine semantics.** Rules read
  head-if-body with mandatory line-by-line connectives, nested
  indentation, and integrity constraints mapped to engine globals;
  assumable unknowns split both ways unless blocked. Arxo's completion
  behavior is its own construct with its own closure rules — compare as a
  pair, not as parity.
- **Mind the version.** The unless-form is documented in the rewritten
  second edition but needs proprietary extensions for some shapes, is
  absent from the first edition's syntax, and is unused by the studied
  model. Evidence from one edition must never be quoted as behavior of
  the other.

## A concrete scenario

The citizenship scenario above runs twelve cases plus the four edits,
comparing signs, grounds, and open-question handling. Logical English also
joins the shared explanation scenario: the same outcome explained three
ways — why yes, why no, and what is missing — under fixed judging criteria.
Limits of the tiny
studied model — one clause, one scene — are properties of that model, not
proven limits of the language, and the page does not present them as such.
An older Prolog formalization of the same article predates Logical English
and is never cited as its result.

## Choosing and combining

Choose Logical English when the authors are lawyers who must read every
rule as a sentence, when explanations must speak in the source's own
words, and when open questions should stay visibly open. Look to Arxo when
burdens need named organs, conflicts need declared priorities, editions
need dating, and derivations need replayable hashes. Combined, controlled
sentences can front the authoring surface while Arxo executes the pinned
meaning behind it — with the template contract, not prose resemblance, as
the binding.

## Evidence and open questions

- Sources checked: September 2026 (both edition repositories with pinned
  commits, the language reference, the studied model file by hash, the
  engine-integration paper, and the official legislation text).
- Studied profile: the first edition at its pin plus the tiny citizenship
  model; the second edition's reference as the version trap above.
- Basis: confirmed by documentation plus a prepared protocol; comparative
  run not performed. The studied model's execution on the pin is
  untestable from here and is not claimed.
- Open: edition-separation discipline on new tasks, and the run itself.

## Sources and reproducible materials

- Shared scenarios: [One charities text, five systems](/comparisons/jersey-charities/) and [Explaining yes, no, and unknown](/comparisons/explanations/).
- First and second edition projects:
  [github.com/LogicalContracts/LogicalEnglish](https://github.com/LogicalContracts/LogicalEnglish)
- Language reference (second edition):
  [LogicalEnglish2 repository](https://github.com/LogicalContracts/LogicalEnglish2)
- Engine-integration paper: [ceur-ws.org/Vol-3193/paper5GDE.pdf](https://ceur-ws.org/Vol-3193/paper5GDE.pdf)
- The studied article (official text):
  [legislation.gov.uk/ukpga/1981/61/section/1](https://www.legislation.gov.uk/ukpga/1981/61/section/1)