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Pattern Logic Primer
Junctives: Monadic Predicates
A logical statement with a union or overlap copula and existential or non-existential quantification of its logical terms is called a Junctive.
Junctives are analogous to the eight forms of a monadic predicate with a bound variable as found in Predicate (First Order, Modern) Logic
Overlap Junctives (Existential Monadic Predicates)
ꓱα [¬β(α)]
ꓱα [¬β(α)]
ꓱα [¬β(α)]
ꓱα ∧ ∄β
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "there exists an alpha, alpha is a not-beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “∀α β(α)”
ꓱα [β(α)]
ꓱα [¬β(α)]
ꓱα [¬β(α)]
ꓱα ∧ ꓱβ
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "there exists an alpha, alpha is a beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “∀α ¬β(α)”
ꓱα [β(¬α)]
∄α ∧ ꓱβ
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "there exists an alpha, not-alpha is a beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “∀α ¬β(¬α)”
ꓱα [¬β(¬α)]
∄α ∧ ∄β
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "there exists an alpha, not-alpha is a not-beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “∀α β(¬α)”
Union Junctives (Universal Monadic Predicates)
∀α ¬β(α)
∀α ¬β(α)
∀α ¬β(α)
∄α ∨ ∄β
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "for all alpha, alpha is a not-beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “ꓱα β(α)”
∀α β(α)
∀α ¬β(α)
∀α ¬β(α)
∄α ∨ ꓱβ
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "for all alpha, alpha is a beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “ꓱα ¬β(α)”
∀α β(¬α)
∀α ¬β(¬α)
∀α ¬β(¬α)
ꓱα ∨ ꓱβ
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "for all alpha, not-alpha is a beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “ꓱα ¬β(¬α)”
∀α ¬β(¬α)
∀α ¬β(¬α)
∀α ¬β(¬α)
ꓱα ∨ ∄β
Alpha is a variable (possible modality) and beta is a predicate (contingent modality). The occasion at the top center of the diagram is the Junctive rendered "for all alpha, not-alpha is a not-beta". This junctive is an accepted theorem (necessary modality).
The involution (De Morgan dual) of this Junctive is “ꓱα β(¬α)”
