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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