Markdown for LLMs
Negation and truth statuses: boundaries
The source Markdown for this article. Copy it into your assistant or download it as a text file.
# Negation and truth statuses: boundaries What the construct does NOT do in 0.2: limits, closed lists, neighbouring constructs, and the selection rule. ## Does not do - **Does not infer absence from silence.** Absence of positive support is Not established, not refuted, not Refuted. Negation-as-failure exists in 0.2 in no form: neither an unfired rule nor `not_known` gives negative support. - **Does not refute through `not_known`.** `not_known(P)` is true on absent support and infers nothing about `P`: the answer on `P` itself stays Not established, not refuted. - **Does not read a conflict by sides.** An atom in Contradiction activates neither `p(x)` nor `not p(x)`; one side is taken only through `supported(P)`. - **Does not apply De Morgan.** `not` is only over an atom; double negation is not eliminated, there is no excluded middle. - **Does not close the world without a holder.** A closure is local (a domain of the same arity), dated (`complete_as_of` is a moment), and optionally windowed (by `effective`); outside the domain — Not established, not refuted. ## Reserved and closed - `opposed`, `conflicted`, `no_evidence` are 0.2 hard keywords: the lexer rejects them as terms, `LDC-E0201`. The Contradiction branch is not read by a separate test in 0.2. - `not_known` is only in a rule body; in a head — `LDC-E1302` (warning: the node is skipped, there is no rule in the compiled output). - Underscore `_` is only a positive body literal; in a head, under `not`, in a status test, and in a case fact — `LDC-E0207`. ## Neighbours and selection rule - `not p` vs `not_known(P)`: established absence with a source vs the “as yet unknown” stage. No source — no `not`. - `not_known(P)` vs `closure`: reading ignorance without a certificate vs a completeness claim with a closure certificate. - Body `not p` vs `refuted(p)`: the same Refuted reading, but the test does not bind variables — a positive conjunct is needed nearby. - Negation vs `unless`/priority: `not` gives negative support and stays silent on Contradiction; a refusal’s victory over a fact is by priority between defeasible rules, not by negation strength (see the pitfalls, item 8).