-- Guide to Ridge Route

DEVICE_O

Start with an elementary associative memory system

Designs and definitions anticipate later devices

Elements

1. Data Field
2. Hardware Realization of the Data Field
3. Terminal Hardware and on_locations
4. Interpretation of the Data Field
5. Commands

Data Field

Data Definition: The Ensemble

An Ensemble is:

• a set {c} of contexts
• a set {d} of details
• a set of ordered pairs of {(c, d)} of contexts and details

• Each context is involved in at least one ordered pair and so is each detail
• The sets {c} and {d} are disjoint (no context is a detail and no detail is a context)
• An ordered pair is sometimes called a structural event or, simply, an event

Hardware realization of the Data Field

• The ensemble corresponds to connections between wires arranged in
  • rows (a, b, c, d and e in the adjacent image) corresponding to contexts and
  • columns (s, t, u, v, w, x, y and z) corresponding to details
• connections are resistances between row wires and column wires
  • each resistance is identical to a standard, e.g. 1 meg-ohm
  • each resistance connects one row wire to one column wire
  • between any particular row wire and any particular column wire there can be 0 or 1 resistances
  • any particular resistance can be inserted or deleted by command of the operator without affecting any other resistance

  

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  Terminal Hardware and On_locations

  Terminal hardware is attached to each wire in one of three modes:

  1. input

  connected to a +dc voltage (same for all inputs)

  2. output

  a current controlled switch (with an ideal 0 impedance) set to close when the current through it is greater than a specified current level, j, set by command (see below)

  in the adjacent image, the status of the output switch is signalled by a "light bulb"

  3. null

  inactive

  

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  When an output switch is closed, it represents an on_location

  E.g, the "light bulb" is lit.

  
  

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  Interpretation of a Data Field

  An interpretation relates an ensemble to a body of experience where each context-detail pair corresponds to an occurrence of structure as described in stage_3 of Water Trail.

  -- Begin Kwik Tour visit

  Example: Keywords in Documents

  Data is notated in two equivalent ways in the adjacent image (also equivalent to the example above)
  • Let (a, b, c, d and e) represent five different documents
  • Let (s, t, u, v, w, x, y and z) represent 8 different keywords appearing in the documents
  • Let each structural event [e.g (a, s)] represent the appearance of a keyword in a document
  • Multiple appearances of a keyword in a document result in but a single structural event
  

  Structural events in the adjacent diagram (arranged for convenience):

  • (a, s), (a, t), (a, u), (a, w)
  • (b, s), (b, u), (b, v), (b, x), (b, y)
  • (c, t), (c, w), (c, x), (c, y),
  • (d, t), (d, u), (d, v), (d, w), (d, y), (d, z)
  • (e, u), (e, v), (e, w), (e, x), (e, y), (e, z)
  
  

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  Commands:

  Each command begins with an initial state and, through operation of the command, produces a final state.

  1. Noticing ; Effacing: [inserting or removing an event (resistance) within an ensemble]

  2. Steps
     • Forward Steps: finding details linked to specified context(s):

       Forward Step: $F1(a)\; =\; (s,\; t,\; u,\; v,\; w)$

       Find all details linked to context a.
       Result: (s, t, u, v, w).

       Document-keyword interpretation: Find all keywords in document a.
       

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       Forward Step: $F2(a,\; c,\; d)\; =\; (t,\; u,\; v,\; w,\; y)$

       Find all details linked to two or more of the contexts a, c, and d.

       Result: t, u, v, w, and y.

       Document-keyword interpretation:
       Find all keywords that appear in two or more of the documents a, c and d.

       How the command works in the hardware:

       1. Set mode switch to input for a, c and d
       2. Set mode switch to null for b and e
       3. Set mode switch to output for all details s, t, u, v, w, x, y and z
       4. Set the trigger voltage for the output switches at 2 milli-amps (for resistances of 1 meg-ohm)
       5. Apply input voltage of 1 volt to operate the device

       In the image, only links participating in triggering an output switch are marked in red
       

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     • Reverse Step: Finding contexts linked to specified detail(s)

       $R4(s,\; t,\; u,\; v,\; w)\; =\; (a,\; d)$

       Find all contexts linked to four or more of the details s, t, u, v, w.

       Result: a and d.

       Document-keyword interpretation: Find documents that contain at least four of the keywords s, t, u, v and/or w.
       

       -- return to Kwik Tour
       

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     • Concatenated Steps

       Output from one step used as input for a second step.

       E.g. $R4F1(\; a\; )\; =\; (a,\; d)$

       Using the examples presented above

       

     • Neighborhoods

       In the example above, d is the nearest neighbor to a

       If contexts are documents and details are keywords, d is the document that is "closest" to document a, based on shared keywords.

       Note that the nearest neighbor of d is e, not a:
       $R5F1(\; d\; )\; =\; (d,\; e)$

       

     • Quasi-simultaneous steps

       Two (or more) steps in the same direction, one after the other, to construct a "union" in the style of set theory

       

  3. Explication

     An orderly reading of the details in a set of contexts according to frequency of appearance.

     Think of approaching a mountainous island by boat: the highest part of the island will appear first, then lower parts of the island in succession.

     $F5(a,\; b,\; c,\; d,\; e)\; =\; Ø$

     F⁴(a, b, c, d, e) = (u, v, w, y)

     F³(a, b, c, d, e) = (t, u, v, w, x, y)

     F²(a, b, c, d, e) = (s, t, u, v, w, x, y, z)

     
     

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     Implication

     An orderly reading of contexts containing details, similar to explication except in the other direction.

     $R8(s,\; t,\; u,\; v,\; w,\; x,\; y,\; z)\; =\; Ø$

     R⁷(s, t, u, v, w, x, y, z) = Ø

     R⁶(s, t, u, v, w, x, y, z) = (d, e)

     R⁵(s, t, u, v, w, x, y, z) = (a, b, d, e)

     R⁴(s, t, u, v, w, x, y, z) = (a, b, c, d, e)

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  Problems interpreted through notation developed in Stage_3 of Water Trail --

  • Legal keywords in cases
  • The legal digest (classes of cases called keynumbers)
  • Case-keywords and case-keynumbers, a problem in multiple ensembles
  • Neighhborhoods and clusters in legal materials
  

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  Forward to Device_1.

  

  

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  All materials copyright by Robert Kovsky, 1997.

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