- Knowledge based agents (RN s6.1)
- more efficient than search since can reason
- KB collection of facts, usually stored as sentences or tables
- Tell, Ask primitives, how does Ask know answers? logical inference
- Example - Wumpus world (RN s6.2)
- Logic (RN s6.3)
- syntax (grammar)
- semantics (meaning)
- correct syntax but not semantics: The smart guitar ran down the cloud.
- inference procedure (proof method)
- Mechanization of logic
- rewrite systems
- syntactical PR
- Rewrite system example
1) A is valid (ie. wff and true) 2) if x, y are valid then xy is 3) [a]xx[b] is valid iff [a][b] is 4) [a]IAI[b] is valid iff [a][b] is 5) [a]xy[b] is valid iff [a]yx[b] is

- Question: is AI valid?
- Forward chaining derivations
- A → AA → AAA → AAAA → etc.
- A → AIAI → AAII → II
- A → AIIA → AIIAAIIA → AIAIAIAI
- Backward chaining attempts
- AI ← A and I - but is I a wff?
- AI ← AIIAI ← AAI - but is AAI a wff?
- AI ← AIAIAI - but is AIAIAI a wff ?
- didn't work since all rules lead to an even number of Is.
- jumping out of system; meta-rules
- Propositional logic
- vs. predicate logic, probabilistic logic, fuzzy logic. etc.
- syntax elements: constants, dummy variables, not and or if iff, parentheses
- can only check veracity of proposition - tautology or satisfiability
- syntax
- BNF metalanguages

sentence ::= atom | complex_sentence atom ::= true, false, P, Q, ... (variables) complex_sentence ::= (sentence) | - sentence | sentence connective sentence connective ::= and or if iff

- true = anything which exists in the world = environment
- false = opposite of true
- P, Q any statement about environment that has true/false answer
- and, or, if, iff (xor) meanings, show if, iff, etc in terms of and/or/not
- 4 possible 1-input/1-output functions, only not nontrivial, truth tables
- 16 possible 2-input/2-output functions (connectives)
- sufficiency - not+and+or, not+and, not+or, nand, nor
- parentheses and conventions
- cnf, dnf, Horn forms (expert systems)

- boolean variables in GF2 (and thus computer software)
- set theory and Venn diagrams
- electronics, eg. relays (and thus computer hardware)

- truth tables
- complexity - 3SAT is NP-complete

- De Morgan rules