Model elimination¶
A goal-directed automated theorem-proving calculus that extends resolution with ancestor links and a chain-based proof state.
Core Idea¶
Model elimination represents clauses as ordered chains, applies extension and reduction steps, and uses ancestor literals to close branches while preserving refutational completeness. Depth-first goal expansion resembles logic programming, while contrapositives and ancestor resolution retain the expressive reach needed for first-order refutation. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of automated reasoning. It is the domain-specific identity determined by a derivation follows the declared chain calculus and closes the initial negated goal under sound extension, reduction, and regularity rules.
Scope of Application¶
Model elimination belongs to automated reasoning and is useful where the analyst can specify the typed automated reasoning carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets, then evaluate a derivation follows the declared chain calculus and closes the initial negated goal under sound extension, reduction, and regularity rules. The scope is broad within that domain but bounded by the need for a derivation follows the declared chain calculus and closes the initial negated goal under sound extension, reduction, and regularity rules. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making a derivation follows the declared chain calculus and closes the initial negated goal under sound extension, reduction, and regularity rules the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Model elimination can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Model elimination. Model elimination compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed automated reasoning carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express a derivation follows the declared chain calculus and closes the initial negated goal under sound extension, reduction, and regularity rules independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of automated reasoning because they reuse the typed automated reasoning carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets, Depth-first goal expansion resembles logic programming, while contrapositives and ancestor resolution retain the expressive reach needed for first-order refutation., and type the carrier, state every parameter and convention in the definition, test that a derivation follows the declared chain calculus and closes the initial negated goal under sound extension, reduction, and regularity rules, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Model elimination Domain-specific
Parents (1) — more general patterns this builds on
-
Model elimination is a kind of Deductive Reasoning Prime
The proposed strict upward parent is
prime:deductive_reasoning.
Hierarchy path (1) — routes to 1 parentless root
- Model elimination → Deductive Reasoning
Neighborhood in Abstraction Space¶
Model elimination sits in a crowded region of the domain-specific corpus (30th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Formal Logic & Type Theory (34 abstractions)
Nearest neighbors
- Well-founded semantics — 0.91
- Proof-theoretic semantics — 0.91
- Constraint satisfaction — 0.90
- Type theory — 0.90
- Reachability problem — 0.90
Computed from structural-signature embeddings · 2026-09-08