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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 

Pattern Logic Terminology for Junctives

Junctives

Overlap Junctive

Overlap Junctive

 Logical statements having only existentially or non-existentially quantified terms, that also have either union or overlap copulas are analogous to one of the eight forms of a monadic predicate with a bound variable in Predicate Logic 

 

Overlap Junctive

Overlap Junctive

Overlap Junctive

A logical statement in which the modal occasion of the copula is limited by the quantified triadic occasions of two logical terms is an overlap.  

A junctive with an overlap copula is analogous to an existentially quantified monadic predicate.

Union Junctive

Overlap Junctive

Union Junctive

A logical statement in which the modal occasion of the copula limits the quantified triadic occasions of two logical terms is a union.  

A junctive with a union copula is analogous to a universally quantified monadic predicate.

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)”

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