General Framework Theory




November 4, 2003


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The Zachman Framework is used as a business framework.  Zachman’s work is well known. 


Figure 1: The Zackman Framework


The Zackman framework is created by taking the descriptive enumeration of the questions:


{ what, how, where, who, when, why },


and “forming a cross product” with the descriptive enumeration of persona roles


{ planner, owner, designer, builder, subcontractor }.


Two lesser-known examples of frameworks are the 12-primitive-element Sowa Framework and 18-primitive-element Ballard Framework for knowledge base construction.  


It is not clear how these frameworks might be used, but if used in a way suggested by the Zackman framework, we would have a means to describe each “event” in terms of some sort of specification of code.


The measurement output from the Ballard Framework has the form of a 19 tuple:


< a(0), a(1), a(2), . .  . , a(18) >


where the value of a(0) is set by a pre-process that categorizes the event that the framework will be used to characterize. 


When any of these frameworks are used, one produces a n-tuple where each element may have a complex form.  By complex form we mean a two level construction having type as one level, of description, and value as the other level of description.  This stratified construction follows the notion that structure and function exists at two different levels of organization.  The function is determined by classes of regularities at the level in which emergence is occurring.  Structure is of those regularities that compose into the thing emerged.


In dynamic complex sets we extend the notion of type to a class and the notion of value to object.


Note that (type:value) extends to (class:object) when the definition of class becomes dynamic.  In very static situations the type is fixed and there are no reasons to have an evolution of the notion of type.  However, in dynamic situations, such as when one does not have sufficient information about possible types and the profile of types are not precisely understood, then one needs to have this dynamic evolution of the complex data set. 


Using frameworks, the type is derived from the semantic primitive’s definition.  The user, or some other means, supplies the value.  The framework offers to the human, or algorithmic process, a theory of semantic primitive.  The user, or algorithm, then supplies specific information into some, but often not all, cells of the framework thus building a classification profile based on the primitives. 


This work suggests the use of the two-level taxonomy as a means to provide classification profiles.


Suppose that 100 events have been considered. 


Domain space = { E(i) | i = 1, . . . , 100 }


A Framework Browser, designed in 2002 by OntologyStream Inc, stores the cell values as strings, and inventories these strings into ASCII text.  A key-less hash table management system exists that governs the access to the data.  The Browser elicits knowledge from the human clerk and then stores this in a convenient way. 


For example:


A parsing program produces a correlation analysis and results in a “derived” 18 tuple:


< a(0), a’(1), a’(2), . .  . , a’(18) >


where a(0) is an event type and a’(1), . . . , a’(18) are each slot-fillers that minimally sign the cell contents. 


The event type can be used to identify a specific taxonomy or framework.   The complex data set has the form (semantic primitive, filler) à  (type, value).  As information become available one can develop a definition of an class from information about the occurrences of the fillers, and the relationships that develop between types. 


The task now is to provide a reification process that develops a good correspondence between classes and object and real world phenomenon. 


The derivation process involved a reification of the slot-fillers in the context of the framework, and this means that a theory of type is developed for each slot and a theory of relationship is develop between various slots.   


In one version of a frame filing process, there is a reduction of a free form of writing to a set of standard fillers for cells.  Over time, the filling of cells is made from a pick list.  But, using community based reconciliation processes there is always a means to introduce new types of fillers at any moment.  A type of “open logic” governs the processes in a Knowledge Operation System.


The set of fillers for each framework cell (a cell is called also a slot in script theory) becomes the set of natural-kind that is observed to be the structural components of the event under consideration. 


These structural components are the substance of events, such as cyber, memetic or genetic expression and the discoveries of relationships between structural elements are achieved using categoricalAbstraction (cA) and eventChemistry (eC) browsers. 


Ontological Primitives, derived by Sowa and Ballard


Linguistic and ontology categorical expression is realized, in natural language, within the co-occurrence of elements of structure and these correlate to functional dependencies between framework slots.  The senseMaking architecture in the OntologyStream Knowledge Operating System (OSI - KOS) is then used to annotate these dependencies and to develop first order logics that provide top down expectancies and predictive filling in of slots (cells) that have not been filled in.   


The slots’ functional dependencies are rendered visually in the framework browsers.


A Predictive Analysis Methodology using cA/eC is fulfilled in a nice way.  Suppose that 100 events have been considered. 


Domain space = { E i | i = 1, . . . , 100 }


In each case, the Ballard Framework has been filled out through:


·        Interactive knowledge elicitation involving human dialog.

·        Some artificial intelligence process that fills in anticipated cell values using a theory of type related to each framework slot.


The domain space is now described by 1900 individual data pieces


{ < a(0), a(1), a(2), . .  . , a(18) >k   | k = 1, . . . , 100  }


where {  a(0) k   | k = 1, . . . , 100  } are the event names, derived by a prior process.


{  a(1) k   | k = 1, . . . , 100  }


are the (1,1,1) cell values of the 3*2*3 matrix that represents the framework, and so on. 

We will use the notation


{  a(i) k   } = {  a(i) k   | k = 1, . . . , 100  },


for a fixed index element i.  The size of the set {  a(i) k   } is less than or equal to 100. 


If values are repeated then the size of this set is smaller, and can be quite small, say 4-10 if values are repeated often.  This reduction in size of sets is due to the naturally occurring data regularity in specific context.


The fundamental enumerations of the 3*2*3 framework matrix is as follows:



independent (I), relative (R), mediating (M)

physical (P), abstract (A)

occurrent (O), continuant (C), universal (U)


The 18 cells are then derived (by Ballard) as


{ process (IPO), script (IAO), object (IPC), schema (IAC), measure (IPU), definition (IAU),

participation (RPO), history (RAO), juncture (RPC), description (RAC), interaction (RPU),relativity (RAU),

situation (MPO), purpose (MAO), structure (MPC), reason (MAC), law (MPU), formalism (MAU) }


The derivation is straight forward, for example “mediating / abstract / universal” is rendered as “law”.  So for each of the 100 events, those aspects of law that are involved in the event is recorded into the (3,1,3) cell.  Ballard justifies this assignment as  “The role played by physical constraints in limiting choice, function, and achievable results.” 



Data regularity within the Ontological Primitives


We are considering the


Domain space = { E i | i = 1, . . . , 100 }


described initially by 1900 individual data pieces


{ < a(0), a(1), a(2), . .  . , a(18) >k   | k = 1, . . . , 100  }


We use the notation


< a(0), a(1), a(2), . .  . , a(18) >k   | i    =   a(i) k


to be the i-th projection of the k-th framework, so


{  a(i) k  } = {  a(i) k   | k = 1, . . . , 100  }


is the set of values that have been placed into the i-th cell across the 100 events.


So the values for “knowledge ending process” are {  a(i) k   }. 


The regularity of the data is then observed empirically when the size of {  a(i) k   } is < 100.


The encoding of this data into type:value pairs enables the graph traversal and both local and global convolutions as defined in the Notational Paper at:



The use of these frameworks may allow one to map







using multiple separate analysis of events - seen from different viewpoints.


A cross level analysis of the relationship between substance and form, from phonology co-occurrence in audio recordings, can also be established as a means to predict function from a partial or incomplete observation of sub-structure.