Monotonicity of entailment¶
A logical property whereby every conclusion entailed by a premise set remains entailed after any additional premises are added.
Core Idea¶
Classical and intuitionistic consequence are monotonic, while default, defeasible and many commonsense reasoning systems are nonmonotonic because added information can withdraw earlier conclusions. A consequence relation checks all models or derivations of the premise set; restricting to models satisfying more premises cannot introduce a countermodel to a conclusion already true in every prior model. 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.
Scope of Application¶
Monotonicity of entailment belongs to logic and is useful where the analyst can specify the typed logic carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate for every premise sets Gamma contained in Delta and formula phi, if Gamma entails phi then Delta entails phi under the same consequence relation. The scope is broad within that domain but bounded by the need for for every premise sets Gamma contained in Delta and formula phi, if Gamma entails phi then Delta entails phi under the same consequence relation. 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 for every premise sets Gamma contained in Delta and formula phi, if Gamma entails phi then Delta entails phi under the same consequence relation 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 Monotonicity of entailment 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 Monotonicity of entailment. Monotonicity of entailment 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 logic carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem.
- Lock the constitutive rule. Express for every premise sets Gamma contained in Delta and formula phi, if Gamma entails phi then Delta entails phi under the same consequence relation independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of logic because they reuse the typed logic carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, A consequence relation checks all models or derivations of the premise set; restricting to models satisfying more premises cannot introduce a countermodel to a conclusion already true in every prior model., and type the carrier, state every parameter and convention in the definition, test that for every premise sets Gamma contained in Delta and formula phi, if Gamma entails phi then Delta entails phi under the same consequence relation, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Monotonicity of entailment Domain-specific
Parents (1) — outgoing typed relations
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Monotonicity of entailment is a kind of Deductive Reasoning Prime
What makes it its own entry: the domain-specific identity determined by for every premise sets Gamma contained in Delta and formula phi, if Gamma entails phi then Delta entails phi under the same consequence relation.
Hierarchy path (1) — routes to 1 parentless root
- Monotonicity of entailment → is a kind of Deductive Reasoning
Neighborhood in Abstraction Space¶
Monotonicity of entailment sits in a crowded region of the domain-specific corpus (15th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Formal Logic & Computation Systems (24 abstractions)
Nearest neighbors
- Paraconsistent logic — 0.93
- Constructive dilemma — 0.91
- Deductive closure — 0.91
- Logical form — 0.91
- Logical equality — 0.90
Computed from structural-signature embeddings · 2026-10-25