Class 5:
Diagrammatic Reasoning Briefly; Resolution;
Midterm

Selmer Bringsjord

• Logistics
  • Project 2: p1 up to and including, I believe, 18.27
  • Project 3: p1
    • ``fancy" options TBA (also: contact me)

• ``Proving" God's existence
• Diagrammatic Reasoning
  • mental imagery: hard!
  • mere diagrams vs. TEMIs
  • BRUTUS.1 ``cheats" -- Weak AI!
  • Hyperproof example_Hyperproof
  • huge opportunities in this area

Remarks on Resolution

$$\begin{array}{ll} \Phi & \mbox{with } \phi \in \Phi\\ \Psi ... ... (\Phi - \{\phi\}) \cup (\Psi - \{\neg \phi\}) &\\ \end{array}$$

$$\begin{array}{c} \phi \vee \psi \quad \neg\psi \vee \chi\\ \hline \phi \vee \chi\\ \end{array}$$

$$\begin{array}{ll} \Phi_1 \cup \{\neg\psi_1, \neg\psi_2, \ldo... ...Phi_1 \cup \Phi_ 2 \cup \cdots \cup \Phi_{n+1} &\\ \end{array}$$

Example from OTTER

---------------- PROOF ----------------

1 [] p|q| -r|s.
2 [] p|q|r.
3 [] -s.
4 [] -q.
5 [] -p.
6 [ur,5,1,4,3] -r.
7 [hyper,2,6] p|q.
8 [hyper,7,4] p.
9 [binary,8.1,5.1] $F.

------------ end of proof -------------

• Midterm review_JR,Ralph
• $\vdots$
• And now the Midterm itself