Masked Disjunction

Also Known As: Inclusive/Exclusive Or Confusion

Formal Fallacy ID: masked_disjunction

Definition

A formal fallacy where the type of disjunction (inclusive vs. exclusive 'or') is misidentified, leading to incorrect elimination of alternatives. In natural language, 'or' is ambiguous, and treating inclusive disjunction as exclusive can invalidate reasoning.

Examples

You can have soup or salad. You chose soup, so you cannot have salad. (But the restaurant meant you could have both.)

The job posting says candidates must have a degree in engineering or five years of work experience. The hiring manager rejects an applicant who has both, reasoning that since they have the degree, the work experience 'doesn't count' — treating an inclusive or as if it were exclusive.

A doctor tells a patient they need to reduce stress or change their diet to improve their health. The patient cuts out junk food and concludes they no longer need to address their stress levels, misreading the inclusive medical advice as an either/or choice requiring only one change.

Formal Logic Pattern

FOL Pattern

The First-Order Logic formula representing this reasoning pattern's logical structure.

FOL (First-Order Logic) uses quantifiers (∀ = for all, ∃ = there exists), connectives (∧ = and, ∨ = or, ⇒ = implies, ¬ = not), and predicates to capture the essential form of a reasoning pattern. For example, the Ad Hominem fallacy: Person(x) ∧ HasFlaw(x) ⇒ Invalid(Claim(x)). These patterns allow automated verification of logical validity.

View in glossary →

(A ∨ B) ∧ A ⇒ ¬B (treating inclusive as exclusive)

Formal Verification: Formally invalid

Verification Steps

Verification Steps

Binary yes/no questions that an AI must answer to detect a reasoning pattern in a text.

Each of the 452 aspects has verification steps — simple yes/no questions designed to systematically detect whether a pattern appears in a text. For ad hominem: "Does the argument attack a person rather than their claim?" For false dichotomy: "Are only two options presented when more exist?" This ensures consistent, reproducible analysis.

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Binary (yes/no) questions an LLM must answer to identify this aspect:

1

Does the argument present alternatives using 'or'?
Type: binary
2

Is the disjunction treated as exclusive when it could be inclusive (or vice versa)?
Type: binary
3

Does the conclusion incorrectly eliminate possibilities based on this misinterpretation?
Type: binary