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03 - Semantic Networks

Semantic networks are a knowledge representation scheme.

This lesson will cover the following topics:

  • Knowlege representations
  • Semantic networks
  • Problem-solving with semantic networks
  • Represent & Reason

Representation

In each knowledge representation, there is a language, and that language has a vocabulary. In addition, the representation contains some content (or knowledge).

Example: Newton's 2nd Law of Motion

$$ F = ma $$ Force is equal to mass times acceleration

Introduction to Semantic Networks

How to represent Raven’s Progressive Matrices using a semantic network. State A, and state B.

  1. Label all objects (x is a circle, y is the diamond, z is the black dot), and reference them as nodes
  2. Represent the relationships between nodes, in both states (frames), both A and B.
  3. Represent the transformation between the nodes between states, A and B.

Structure of Semantic Networks

  • 1. Lexically: nodes
  • 2. Structurally: directional links
  • 3. Semantically: application-specific labels

Characteristics of Good Representations

  • Make relationships explicit
  • exposese natural contraints
  • bring objects and relations together
  • exclude extraneous details
  • transparent, concise, complete, fast, computable

Guards and Prisoners Problem

Description

  • Three guard and three prisoners must cross river.
  • Boat may take only one or two people at a time.
  • Prisoners may never outnumber guards on either time (thought prisoner may be alone on either coast).

Modeling using Semantic Nework

Lexicon: Consider each node to be a unique state, represented by: - number of prisoners and guards on left side - number of prisoners and guards on right side - side that boat is on.

Structure:

Semantic:

Inference about State Transitions?

Which transitions (e.g. moves) between states are both legal AND productive? Represent total possible states given transformations possible:

i 0 1 2 3 4 6 7 8 9 10 11 12
trans: init:< 2p to R:> p to L:< 2p to R:> p to L:< 2g to R:> g.p to L:< 2g to R:> p to L:< 2p to R:> p to L:< 2p to R:<
\(g_i\) 3, 0 3, 0 3, 0 3, 0 3, 0 1, 2 2, 1 0, 3 0, 3 0, 3 0, 3 0, 3
\(p_i\) 3, 0 1, 2 2, 1 0, 3 1, 2 1, 2 2, 1 2, 1 3, 0 1, 2 2, 0 0, 3

Choosing Matches by Weight

One can weigh transformations to favor specific types of transformations over others. For example:

Points Weights

  • 5: Unchanged
  • 4: Reflected
  • 3: Rotated
  • 2: Scaled
  • 1: Deleted
  • 0: Shape Changed

04 - Generate and Test

Lesson preview:

  • Generate and test method
  • Smart Generators
  • Smart Testers
  • Examples

Generators and Testers

Smart Generator

Takes one state, and generates all possible states, however, should not generate states that are not productive.

Smart Tester

Analyzes all generated states, and filters to only legal (i.e., those states that adhere to logical constraints) and productive (i.e., resultant states that have not yet been observed) states.

Note: For each problem, we have to find the right balance the smartness of generators and testers.

Generate and Test for Raven's Problems

Explicity

  1. Setup semantic network for A and B, and construct transformation.
  2. Apply transformation to C to generate D
  3. Compare D to possible solutions and find highest match (via level of confidence).
  4. Ensure that D meets a confidence level threshold.
  5. If not, repeat 1-4, however using new semantic network construction approach.

Implicitly