Class 6:
Indexing; Unify; Nothing New in Semantic Nets, etc.; Guess Who?; Planning

Selmer Bringsjord

Logistics

• Make sure you're using our web site!
• Project 2 out:
  • up to and including 18.27
  • Supererogatory options:

• Project 3: (p1) done
  • Advanced options:
    • grad students pick project for group that relates to your company (run by me)
    • simple version of Hyperproof using a TP
    • $\vdots$

• Why Lisp? -- we haven't talked about this, and we won't!
  • Built-in support for lists
  • Automatic storage management
  • Dynamic typing
  • First-class functions
  • Uniform syntax
  • Interactive environment
  • extensibility

• Answers to the Midterm: later!_Ralph
• Second offer of automatic A (recall Collatz's problem)
  • First: infinitude_Hyperproof
  • Formal diagnosis:
    • so there is a set $\Gamma$ of first-order formulas such that $\cal I$ $\models \Gamma$ iff $\cal I$ is infinite
  • What about finitude? Can it be expressed in FOL? I.e., is there a set that can play an analogous role for finitude?

• Indexing $\ldots$
• The unification algorithm $\ldots$
• Frame systems and semantic networks are just FOL $\ldots$
• You need to learn the foundation, FOL, inside and out!

• Planning as simply theorem proving
• initial state:
  • $\alpha_1[s_0] \wedge \alpha_2[s_0] \ldots \alpha_n[s_0]$
• operators as successor-state axioms:
  • $\forall a, s \mbox{ {\em Have(Milk,Result(a,s))}} \Leftrightarrow$
  • $\mbox{{\em ((a = Buy(milk)}} \wedge \mbox{{\em At(Supermarket,s))}}$
  • $\vee \mbox{ {\em (Have(Milk,s)}} \wedge \mbox{{\em a $\not=$\space Drop(Milk))}})$
• Given this, simply:

  $\vdash \exists p G(\mbox{{\em Result}}'(p,s_0)) ?$

• Next: more efficient representation schemes & POP

  

Figure 1: Table for Indexing.

  

Figure 2: Unification Algorithm.

  

Figure 3: Simple Planning Agent.