Download Propositional Calculus - Syntax

Artificial Intelligence: Definition
“... the branch of computer science that is concerned
with the automation of intelligent behavior.” (Luger,
2009)
“The science and engineering of making intelligent
machines” (McCarthy, 2007)
“The art of creating machines that perform functions
that require intelligence when performed by people”
(Kurzweil, 1990)

Artificial Intelligence: Definition
What is Intelligence?
Is intelligence monolithic or diverse?
Is there a range of intelligences?
Must one be human to be intelligence?
What is artificial?
Computers?
 Simulations?
Is there a difference between thinking intelligently
and acting intelligently?

Acting Humanly
The Turing Test: A
human judge converses
with a human and a
machine that pretends
to be human in natural
language .
Thinking Humanly
The machine thinks in the same way as a human,
passes psychological tests.
Must it have the same sensory capability?
Does this require simulation of the brain?
Should the machine have the same limitations as a
human?
Cognitive Science, Neural Net Simulations
Acting Rationally
Rational Agent:
Interacts with environment
Has goal or goals to achieve
Measured against optimal results (infinite
computational ability, omniscience)
Thinking Rationally
Formal reasoning
Logic: Proposition, Predicate, Non-monotonic,
Temporal
Mathematical Deduction
Computational Limitations
Focus on Reasoning, not Knowledge
Early Work
Focused on rules, game-playing, heuristics
Game Playing: Checkers
GPS (General Problem Solver)
SHRDLU (Block world)
Perceptrons
Resolution
SIR (Question Answering)
LADDER (Natural Language front-end for DBs)
Paradigm Shift
“Knowledge is power”
Expert Systems
Incorporate knowledge from domain experts
Knowledge base more important, deduction engine
less important
Introduce and measure uncertainty

Key Areas
Deduction
Search
Knowledge Representation
Perception
Planning
Learning
Natural Language
Robotics

Approaches
Symbolist
Logic
Rule-Based, Case-Based
Sub-Symbolist
Neural Nets
Cognitive Simulation
Stochastic
Bayesian Belief Networks
Markov Chain Monte Carlo

Philosophical Issues
Can only humans think?
Asking if machines can think is like asking if
submarines can swim (Minsky)
If computers can only following their programming,
how can they be creative?
Must machines think like humans?
Ethic questions

Propositional Calculus
Propositions are statements that must be true or false
- “It is raining” “George W. Bush is President”
Sufficient context is assumed to make statements
unambiguous (now, of the US...)
Propositions are represented by letters, P, Q, R, S...
May be combine by Boolean operators to make
more complex statements (formulas)

Boolean Operators
¬ Negation, not
⋀ Conjunction, and
⋁ Disjunction, or
→ Implication, if then
↔ Double implication, if and only if
⊗ Exclusive Or

Negation is a unary operation, all others are
binary.
Propositional Calculus - Syntax
Proposition symbols: P, Q, R, S (variables whose
values are true or false)
Truth symbols: true, false
Well-formed formula (WFF): A proposition symbol,
truth value, or (¬ formula), or (formula op formula)
where op is one of ⋀, ⋁, →, ↔,⊗.
These are the only formulas.

Propositional Calculus - Syntax
Order of precedence:
The operators have different levels of precedence
with negation binding more tightly, and exclusive or
least tightly (in the order given on a previous slide).
We only use parentheses to change the normal order
of precedence.
Propositional Calculus - Semantics
An interpretation assigns a truth value (T or F) to
each propositional symbol in a formula.
Formulas are evaluated recursively:
A propositional symbol's value is given by the
interpretation
A truth symbol's value is T for true and F for false
For a complex formula, first evaluation the
operand(s) and then apply the operator according
to its truth table.

P
∨
Q
∧
Q
⊗
Truth Tables
P
T
T
F
F
Q
T
F
T
F
P
P
T
T
F
F
Q
T
F
T
F
P
T
F
F
F
F
T
T
F
P
T
T
F
F
Q
T
F
T
F
P ⌐P
T F
F T
T
T
T
F
P
T
T
F
F
Q
T
F
T
F
P→Q
T
F
T
T