Possible-World Case Matrix¶
Template — instantiates Necessity-Possibility-Contingency Framing
A matrix that compares accessible alternative cases while controlling which assumptions vary.
Possible-World Case Matrix arrays several admissible cases side by side as columns and reads a conclusion across all of them at once. Its defining move is the disciplined variation of assumptions: some assumptions are held fixed down every column and one or a few are varied across columns, so that when a conclusion holds in all admitted cases it is necessary within the frame, in some it is contingent, and in none it is impossible. Where a claim ledger takes propositions one at a time, this matrix is inherently comparative — it exists to show which conclusions survive as the varied assumptions move, and which were only ever propped up by a single convenient case.
Example¶
A regional grid planner is deciding whether the network can absorb a new 400 MW wind farm without upgrading a transmission corridor. Rather than argue over one "typical" day, the planner builds a Possible-World Case Matrix. The columns are admitted operating cases supplied by an accessibility rule — high-wind/low-demand spring night, peak summer afternoon, peak summer with one corridor line out for maintenance, low-wind winter evening. Fixed down every column: the existing generation fleet, the line ratings, the conservation and capacity constraints. Varied across columns: wind output, demand level, and which line is in service.
Reading the conclusion "no upgrade needed" across the row shows it holds in three cases but fails in exactly one — peak summer with a line out. The matrix has converted a yes/no fight into a precise finding: the upgrade is not necessary, it is contingent on the single-contingency summer-peak case, and the dependency map points straight at the assumption (N-1 during peak) that flips it. That is a scheduling and reliability question, not a build-everything question.
How it works¶
Columns are the admitted cases; rows are the assumptions and the conclusions being tracked. The method is to partition assumptions into held and varied before any case is filled, then populate each column consistently and read conclusions horizontally. The payoff is the dependency reading: for each conclusion the matrix records which varied assumption its truth-value tracks, so "contingent" is never left vague — it names the assumption it is contingent on. The matrix consumes an accessibility rule that says which cases are admissible; it does not manufacture that rule, so a case only appears if the supplied rule lets it in.
Tuning parameters¶
- Case-set size — few sharp columns versus many. More columns cover the space but dilute attention and invite possibility inflation; too few hide the case that flips the answer.
- Held-versus-varied split — which assumptions are frozen and which move. Varying too many at once makes a flipped conclusion un-attributable; varying too few hides real contingencies.
- Case spacing — clustered near a base case versus spread to the boundaries. Boundary cases stress-test; clustered cases refine.
- Conclusion set — how many conclusions are tracked across the same columns before the grid becomes unreadable.
- Fill fidelity — quick qualitative marks versus modeled values per cell; fidelity buys trust at the cost of effort.
When it helps, and when it misleads¶
Its strength is separating the necessary from the merely-usually-true: a conclusion that survives every admitted column is robust in a way no single case can show, and one that fails in a lone column exposes exactly the assumption a plan hangs on. It is the natural home for the Kripke-style intuition that necessity is truth across all accessible worlds[1].
Its failure mode is that the answer lives or dies by the case set, and the case set is chosen. A conclusion "survives every case" only because every inconvenient case was silently left out — a too-narrow accessibility rule manufactures a false necessity, while an unbounded one inflates the possibility space until the matrix says nothing. The classic misuse is padding the columns with near-duplicate friendly cases and omitting the one adverse case everyone can already picture. The guarding discipline is to justify the accessibility rule out loud and to require at least one column chosen specifically to break the conclusion.
How it implements the components¶
possible_world_or_case_set— the columns are the concrete case set; building and populating them is the matrix's primary output.assumption_context_frame— the held-versus-varied partition records which assumptions are fixed down every column, keeping the comparison honest.contingency_dependency_map— reading each conclusion across columns yields the map of which conclusion depends on which varied assumption.
It does not classify claims or hand down action rules — modal_status_taxonomy and decision_translation_rule belong to its nearest twin, Modal Claim Table, which the matrix feeds rather than replaces; and it does not author the admissibility rule or ladder constraint relaxations — accessibility_relation_or_constraint_rule and assumption_relaxation_ladder are Design Constraint-Relaxation Table's, supplied to the matrix as an input.
Related¶
- Instantiates: Necessity-Possibility-Contingency Framing — the matrix is the comparative grid that separates necessary conclusions from contingent ones.
- Consumes: Design Constraint-Relaxation Table supplies the accessibility rule that decides which cases are admissible columns.
- Sibling mechanisms: Modal Claim Table · Counterfactual Minimal-Change Checklist · Assumption Lock-and-Relax Workshop · Necessity-Possibility Red Team · Legal Obligation-Permission Matrix · Modal Language Review Protocol
Editorial Notes¶
Form Classification¶
Form family: Representation, Specification & Plan
Rationale: Possible-World Case Matrix operates as a static representation, map, specification, schema, or prospective plan that externalizes information because it a matrix that compares accessible alternative cases while controlling which assumptions vary.
Independent corroboration: The frozen evidence defines Possible-World Case Matrix as 'A matrix that compares accessible alternative cases while controlling which assumptions vary', so its operative form is Representation, Specification & Plan.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Philosophy
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Multi-domain
Rationale: Reasoning across accessible alternative worlds while holding assumptions controlled descends from modal logic and analytic philosophy.
Related originating lineages:
- Mathematics — Mathematics supplies the formal relational semantics and matrix-like systematic variation.
Review resolution: Both blind reviewers agree that philosophy is the primary origin. Reconciliation resolves encyclopedia synthesis disagreement. Formative alternate lineages are retained as mathematics; later breadth of use is recorded separately as domain_reach=multi_domain, while origin_mode=cross_disciplinary_synthesis describes the relationship among origin lineages.
Encyclopedia synthesis: The exact catalogued form synthesizes established practice rather than reproducing a single standard historical label.
Review outcome: Reconciled after independent review; high confidence.
References¶
[1] Kripke, S. A. "Semantical Considerations on Modal Logic". Acta Philosophica Fennica 16, 83–94 (1963). Gives Kripke-style semantics in which necessity at a world requires truth throughout the worlds accessible from it. registry ↩