1. EA C461 – Artificial Intelligence Logical Agent
S.P.Vimal

2. To discuss… Forward Chaining Backward Chaining DPLL Algorithm
WALKSAT Algorithm
Vimal EA C461- Artificial Intelligence

3. Forward and backward chaining
Horn Form (restricted)
KB = conjunction of Horn clauses
Horn clause =
proposition symbol; or
(conjunction of symbols)  symbol
E.g., (C  B  A)  (C  D  B)
Definite clause
Horn Clause with exactly one +ve literal
Fact
Horn Clause With no negative literal
Integrity constraints
Horn Clause With no positive literals
Vimal EA C461- Artificial Intelligence

4. Forward and backward chaining
Modus Ponens (for Horn Form): complete for Horn KBs
α1, … ,αn , α1  …  αn  β Β
Can be used with forward chaining or backward chaining.
These algorithms are very natural and run in linear time
Vimal EA C461- Artificial Intelligence

5. Forward chaining
Idea: fire any rule whose premises are satisfied in the KB,
add its conclusion to the KB, until query is found
Vimal EA C461- Artificial Intelligence

6. Forward chaining algorithm
Forward chaining is sound and complete for Horn KB
Vimal EA C461- Artificial Intelligence

7. Forward chaining example
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8. Forward chaining example
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9. Forward chaining example
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10. Forward chaining example
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11. Forward chaining example
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12. Forward chaining example
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13. Forward chaining example
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14. Forward chaining example
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15. Forward chaining
Every inference is essentially an application of modus ponens  sound, complete.
Inferred table reaches a fixed point, from which no new inferences are possible.
Data-driven reasoning
Focus of attention starts from the known data
Incremental forward chaining
Vimal EA C461- Artificial Intelligence

16. Backward chaining Idea: work backwards from the query q:
to prove q by BC,
check if q is known already, or
prove by BC all premises of some rule concluding q
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17. Backward chaining example
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18. Backward chaining example
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19. Backward chaining example
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20. Backward chaining example
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21. Backward chaining example
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22. Backward chaining example
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23. Backward chaining example
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24. Backward chaining example
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25. Backward chaining example
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26. Backward chaining example
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27. Efficient propositional inference
Two families of efficient algorithms for propositional inference:
Complete backtracking search algorithms
DPLL algorithm (Davis, Putnam, Logemann, Loveland)
Incomplete local search algorithms
WalkSAT algorithm
Vimal EA C461- Artificial Intelligence

28. Recall that…
Satisfiability is connected to inference via the following:
KB ╞ α if and only if (KB α) is unsatisfiable
We will learn two class of propositional inference algorithms on model checking based on
Back tracking search
Local search
These algorithm checks for satisfiablity of a sentence
Vimal EA C461- Artificial Intelligence

29. DPLL algorithm
Determine if an input propositional logic sentence (in CNF) is satisfiable.
Improvements over truth table enumeration:
Early termination
A clause is true if any literal is true.
A sentence is false if any clause is false.
Pure symbol heuristic
Pure symbol: always appears with the same "sign" in all clauses.
e.g., In the three clauses (A  B), (B  C), (C  A), A and B are pure, C is impure.
Make a pure symbol literal true.
Unit clause heuristic
Unit clause: only one literal in the clause
The only literal in a unit clause must be true.
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30. DPLL algorithm
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31. WalkSAT algorithm Incomplete, local search algorithm
Evaluation function: The min-conflict heuristic of minimizing the number of unsatisfied clauses
Balance between greediness and randomness
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32. WalkSAT algorithm
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33. WalkSAT algorithm More useful when we expect a solution to exist
Is the algorithm complete?
Detecting unsatisfiablity is a problem …
We need to determine unsatisfiablity to determine entailment 
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34. Hard satisfiability problems
Consider random 3-CNF sentences. e.g.,
(D  B  C)  (B  A  C)  (C  B  E)  (E  D  B)  (B  E  C)
m = number of clauses
n = number of symbols
Hard problems seem to cluster near m/n = 4.3 (critical point)
Nearly satisfiable / nearly unsatisfiable
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35. Hard satisfiability problems
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36. Hard satisfiability problems
Median runtime for 100 satisfiable random 3-CNF sentences, n = 50
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37. Hard satisfiablity problems
Problems near the critical point are difficult to solve comparing to the random instances
DPLL is quite effective, averaging few thousands steps comparing to the 1015 for TTE.
Of course, WALKSAT is even faster.
Vimal EA C461- Artificial Intelligence

38. Summary
Logical agents apply inference to a knowledge base to derive new information and make decisions
Basic concepts of logic:
syntax: formal structure of sentences
semantics: truth of sentences wrt models
entailment: necessary truth of one sentence given another
inference: deriving sentences from other sentences
soundness: derivations produce only entailed sentences
completeness: derivations can produce all entailed sentences
Wumpus world requires the ability to represent partial and negated information, reason by cases, etc.
Resolution is complete for propositional logic Forward, backward chaining are linear-time, complete for Horn clauses
Propositional logic lacks expressive power
Vimal EA C461- Artificial Intelligence