Class 3:
First-Order Logic

Selmer Bringsjord

Misc. Logistical Issues

• Again: class pictorial roster, w/ email addresses & web sites_w
• TA Selim's info now in syllabus, w/ office hrs_w
• My office hrs now in syllabus as well_w
• Go page_w
• ``The Lost Episode" (propositional calculus)$\ldots$

GUESS WHO?

Foundation for Logic-Based Agents

• Knowledge-Based Agent pseudo-code_h
• The wumpus-world sequence 6.2 $\rightarrow$ 6.4_h
• Two central equation-schemas:
  • KB $\models \alpha$
  • KB $\vdash_i \alpha$

The Golden Concepts

• We've mentioned the three programming paradigms
• Two AI paradigms: logicist or symbolicist vs. connectionist or sub-symbolicist
• A list of key ``golden" concepts for logicist paradigm:
  • soundness; proof; completeness; proof theory; interpretation; compositionality; deduction; validity ( $\models \alpha$); satisfiability; unsatisfiability

Getting Help From Hyperproof

• HYPERPROOF_Hyperproof
  • Selmer's World$\ldots$
  • NBA 1999

ENGLISH	FOL
Names:
Selmer	a
Conrad	c
Olga	b
Katherine	n1
Alexander	n2
Predicates:
x is rich	Large(x)
x is missing brain	Tet(x)
x is richer than y	Larger(x,y)
x lives further upstate than y	BackOf(x,y)
x lives between y and z	Between(x,y,z)
x is a parent of y	Likes(x,y)
x is a child	Small(x)
x is happy	Happy(x)
x and y live together	SameRow(x,y)

Higher-Order Logic

• Hey, not so fast R&N!
• Define identity
• E.g., ``There is a notworthy property Selmer and Conrad share."
• SNePSLOG (possible 1 credit ind st investigation)
• The $\lambda$ operator
• $\lambda$x, y Gender(x) $\not=$ Gender(y) $\wedge$ Address(x) = Address(y)
• Basically same in Lisp $\ldots_{JR9000}$

Some Lisp$\ldots$

• JR9000's gentle questions
• Ralph's not-so-gentle game
• True randomness? An automatic A?
• Collatz' function$\ldots_h$

Collatz' Function

$$c(n)=\left\{ \begin{array}{ll} n & \mbox{if $n = 0 \vee n = 1... ...$n$ is even}\\ 3n + 1 & \mbox{otherwise} \end{array} \right.$$

• Conjecture: Starting from any positive integer n, repeated iteration of this function eventually produces the value 1.
• Lisp$\ldots$

Mental Objects

• The problem w/ straight FOL in connection w/ beliefs
• The detective story example
• A driving example (extemporaneous)
• Russell & Norvig's Treatment of Mental Objects - any good?
• CYC and Problem 8.15

  

Figure 1: Generic Logic-Based Agent.

  

Figure 2: Typical Wumpus World.

  

Figure 3: First Step By Agent in WW.

  

Figure 4: Later Stages of Agent in WW.