Logical possibility¶
The status of a proposition that is satisfiable or at least not refutable under the axioms, inference rules, semantics, and consistency policy of a specified logical system.
Core Idea¶
Logical possibility is the status of a proposition that has an admissible interpretation—or otherwise cannot be refuted—under the axioms, inference rules, semantics, and consistency policy of a specified logical system and background theory. The background matters. The background matters.
Scope of Application¶
Logical possibility is used in modal logic, model theory, proof theory, formal verification, mathematics, philosophy, knowledge representation, counterfactual analysis, and consistency arguments. Use it with formal language and translation, proposition, logic and background axioms, proof and semantic consequence, admissible models/worlds and accessibility, consistency/explosion policy, decision and completeness assumptions, witness model or derivation, computational limits, and an explicit boundary from physical, metaphysical, epistemic, technological, practical, and probabilistic possibility. Record unresolved rather than possible when proof search or formalization is incomplete.
- Model theory. Finds satisfying structures.
- Modal logic. Evaluates accessible worlds.
- Proof theory. Tests derivability/consistency.
- Verification. Searches reachable satisfying states.
- Foundations. States relative consistency.
Clarity¶
Report formal language, proposition translation, logic, axioms/background theory, semantics and admissible models/worlds, accessibility relation if modal, proof calculus, consistency/explosion policy, decidability/completeness, witness model or derivation, tool bounds, and exact contrast with physical/metaphysical/epistemic possibility. The closest near miss sets the boundary: Metaphysical possibility is the closest philosophical neighbor; it may use modal logic but adds claims about what could exist beyond formal satisfiability. A positive case must satisfy this test: A proposition is logically possible relative to a declared system/theory when it has an admissible model or otherwise survives the system's accepted refutation criterion.
Manages Complexity¶
One ordinary-language ‘could’ can hide multiple modalities. Formalization compresses them into a satisfiability question but introduces dependence on theory, semantics, and metatheory. The central framework precision–ordinary-language breadth tradeoff is this: Formal systems decide clear formulas while translation can omit intended constraints. A second non-refutation–positive witness tension matters because Failure to disprove is weak while a model demonstrates satisfiability. The system relativity–modal overreach tension adds that A result is valid in one logic while rhetoric suggests unrestricted possibility.
Abstract Reasoning¶
Use three linked moves: formalize the proposition without changing its modality; fix the logic and background theory; seek an admissible model or a refutation under sound rules. As a collapse test, the case exits when the system or background assumptions are unspecified or when mere non-discovery of contradiction is treated as a completed decision. A fourth check is to audit consistency, completeness, and computational limits. A final check is to state only the system-relative result and its modal boundary.
Knowledge Transfer¶
Satisfiability reasoning transfers among formal domains, but axioms, model classes, and accessibility relations must be remapped. No conclusion about physical realization follows automatically. No canonical parent prime is currently asserted; broader structural comparisons remain related-prime analogies until separately adjudicated in the DAG. The portable structural comparison. Necessity requires truth in all relevant interpretations, not one.
Relationships to Other Abstractions¶
Current abstraction Logical possibility Domain-specific
Parents (1) — more general patterns this builds on
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Logical possibility is a kind of Modal Status Domain-specific
Logical possibility satisfies the defining boundary of Modal Status: A modal status is the classification of a proposition, state of affairs, event, or world as actual, possible, necessary, contingent, or impossible relative to specified accessibility, logical, metaphysical, temporal, epistemic, or normative semantics.
Hierarchy path (1) — routes to 1 parentless root
- Logical possibility → Modal Status
Neighborhood in Abstraction Space¶
Logical possibility sits in a crowded region of the domain-specific corpus (19th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Logical Inference, Modality & Conditional Structures (27 abstractions)
Nearest neighbors
- Obligationes — 0.91
- Constructional System — 0.91
- Modus ponens — 0.90
- Alternative facts — 0.90
- Cambridge change — 0.90
Computed from structural-signature embeddings · 2026-10-08