Signed in as:
filler@godaddy.com
Signed in as:
filler@godaddy.com
The organizing principle of every pattern is limitation.
Limitation is a relation between a portion and an extent.
The portion and extent can be either:
We may visualize limitation as one shape being bounded by another.
If a jigsaw puzzle piece is a portion and the remainder of the puzzle is an extent then the piece's presence in the puzzle is a limitation.
The portion cannot exceed the extent, but the extent need not be any more than the portion (.ie a puzzle of one piece)
We are not speaking of sets, but we need a symbol for limitation, and this one comes close enough.
An ADEPT LION occasion is a synthesis of its inputs. These inputs are the occasions at the other end of its channels. The synthesis consists of limitations. These limitations are interpreted in a process much like an algebraic calculation in mathematics. But rather than numbers, there are occasions of pattern. And rather than multiple operations like addition and multiplication, there is only limitation. And just as there are laws in mathematics to govern the use of operations (.ie associative, commutative), there are laws in pattern language to govern the operations of limitation.
A Limitation: ⊇
An Occasion: a Greek letter like "α"
Absence of an occasion: ∅
An occasion that limits itself entails itself
α ⊇ α
⊢ α
An occasion that limits no occasion entails its complement.
α ⊇ ∅
⊢ ¬α
An occasion that is limited by no occasion entails the selection of itself.
∅ ⊇ α
⊢ [α]
No occasion, being both limited by an initial occasion, and limiting another subsequent occasion, entails that the initial occasion does not limit the subsequent occasion.
α ⊇ ∅ ⊇ β
⊢ α ⊉ β
An occasion, which is limited by one occasion and limits another entails that the central occasion is an approximation of the limitation that exists between the other two occasions.
α ⊇ β ⊇ γ
⊢ β ≈ α ⊇ γ
No occasion, being simultaneously limited by two occasions entails the complement of either of these occasions limiting the other.
α ⊇ ∅ ⊆ β
⊢ ¬α ⊇ β
⊢ α ⊆ ¬β
No occasion, simultaneously limiting two occasions entails the complement of either of these occasions is limited by the other.
α ⊆ ∅ ⊇ β
⊢ α ⊇ ¬β
⊢ ¬α ⊆ β
An occasion, simultaneously limited by two occasions entails that the central occasion is an approximation of the overlap of the other two occasions.
α ⊇ β ⊆ γ
⊢ β ≈ α ∩ γ
⊢ β ≈ γ ∩ α
An occasion, simultaneously limiting two occasions entails that the central occasion is an approximation of the union of the other two occasions.
α ⊆ β ⊇ γ
⊢ β ≈ α ∪ γ
⊢ β ≈ γ ∪ α
An occasion, that limits some other occasion entails that the other occasion is limited by the initial occasion.
α ⊇ β
⊢ α ⊇ β ⊆ α
⊢ β ⊆ α ⊇ β
⊢ β ⊆ α
When the limitation laws are applied sequentially, they are necessary and sufficient to derive interpretations for all of the pattern occasion types that the fixed schema of the ADEPT LION pattern language establishes.
The compound application of the laws in an act of interpretation is called a sequence.
Copyright © 2024 Pattern's Language - All Rights Reserved.
ADEPT LION is a Salveretec PBC patented invention