Unraveling the Mysteries of Artificial Intelligence

1. Aside on AI • Will computers ever be intelligent? • Really intelligent? • Tasks that previously were thought to require intelligence: • adding and subtracting • playing chess • driving a car • recognizing speech or handwriting • translating to a foreign language • proving mathematical theorems • What does it mean to say that a computer is intelligent? • Is that the same as being a person? What is a person? • Is a computer program a person? • Is a person a computer program?

2. Achieving “Intelligence” • How do AI program achieve “intelligent” behavior? • Currently, three main paradigms: • Neural Nets • Genetic Algorithms • Symbolic knowledge representation and search

3. Neural Nets • Model behavior of neurons • Each neuron has many Inputs • Output is weighted sum of inputs • Training: adjusting the weights to improve behavior • Learning: networks improve performance with time • Feedback: large networks with feedback have very complicated behavior (pondering? dreams?) • Success: many (small) problems are handled well; bigger problems are problematic

4. Genetic Algorithms • Many similar simulated organisms, each with its own program governing behavior • The organisms are run for a time, and their behavior is measured for fitness • The more successful organisms are more likely to cross (reproduce) • Random mutations can also be introduced in the programs • Each generation tends to have more successful behavior than the last, on average • Results: good for some optimization problems

5. Symbolic AI • Represent a problem as a collection of logic (symbolic) statements • Characterize the initial condition symbolically • Characterize goal state symbolically • Characterize actions that are possible in the world as productions or changes to the initial condition • Search through possible actions to find a path to the goal

6. Search in Artificial Intelligence • Represent your problem as a graph where nodes are states and edges are operators that go between states • Define problem states (nodes) • Identify start and goal states • Define operators (edges) • Use DFS or BFS to find goal • Example: Missionaries and cannibals problem • states: (3,3,1)  3 missionaries, 3 cannibals, and 1 boat on left side of river. • Operators: one or two people cross the river in the boat, so that there isn’t a cannibal majority on either side. • Goal: get to the other side? • Moves? • (331)–(220)–(321)–(210)–(221)–(020)–(031)–(010)–(021)–(000)

7. Game Playing • We could use DFS but…can’t search whole tree! • limit depth of search and use an evaluation function • We could use DFS but…how do we know which move the opponent will choose? • minimax algorithm: assume the opponent does what looks best. • i.e. at nodes where it is the human’s turn, pick the move that looks best for human. Where computer’s turn, pick the move that looks best for the computer

8. DFS/BFS Resource Requirements • DFS: • Runtime? O(n), n=number of nodes expanded • Space required? O(d), d = depth of search • Can I cut off a search after 3 seconds? • BFS: • Runtime? O(n) • Space required? O(breadth of tree) = O(bd), b=branching factor • Can I cut off a search after 3 seconds? • Staged DFS: do a DFS of depth 1, 2, 3, … until out of time • Runtime? O(n) • Space required? O(d)

9. Mankalah • An ancient gamed called Kalah or Mankalah uses stones and pits: 6 to a side and one on each end. • 4 stones are initially placed in each side pit. None are in the end pits (called Kalahs – a player’s kalah is on her right). • A move consists of picking up the stones in a pit and distributing them, one at a time, in successive pits. • If the last stone is placed in your Kalah, you go again • If the last stone is placed in an empty pit on your side, you capture the stones in that pit and the opposite one, on the opponent’s side of the board. These are put into your Kalah. • The game ends when one player has no stones left; the other player puts all the remaining stones on her side into her Kalah. • Whoever ends with more stones in her Kalah wins.  Can you make your Kalah program smarter than Bonzo?

10. Mankalah minimax Result minimaxVal(Board b, int d) // d is depth if (b.GameOver() or d==0) return new Result(0, evaluate(b)) if (b.whoseMove()==Board.TOP) //TOP is MAX bestVal = -infinity for (move=first; move<=last; move++) if (b.legalMove(move) [and time not expired]) Board b1 = new Board(b) //duplicate board b1.makeMove(move) //make the move val=minimaxVal(b1,d-1) //find its value if (val>bestVal) //remember if best bestVal=val; bestMove=move else // similarly for BOTTOM’s move return new Result(bestMove,bestVal);

11. Heuristic Search Techniques • What do you do when the search space is very large or infinite? • We’ll study three more AI search algorithms: • Backtracking search • Greedy search (Best-first) • A*

12. Example: the 8-puzzle • How would you use AI techniques to solve the 8-puzzle problem?

13. Symbolic AI solution • Start state: 5 4 0 6 1 8 7 3 2 (e.g.) • Goal state: 1 2 3 8 0 4 7 6 5 • Edges: sliding a tile. From start state: • 5 4 8 6 1 0 7 3 2 • 5 0 4 6 1 8 7 3 2 What search algorithm should I use?

14. Backtracking search • Start at the start state • Search in any direction • Backtrack when stuck • This is really the same as • Used very frequently • E.g. Perl regular expression matching • E.g. finding a traveling salesman’s circuit • E.g. graph coloring Depth-first search Is there any way I can be smarter than a blind search?

15. How to get from Arad to Bucharest? • How to get from Isai to Fagaras?

16. Greedy Search (Best-first) • Best-first search: like DFS, but pick the path that gets you closest to the goal first • Need a measure of distance from the goal h(n) = estimated cost of cheapest path from n to goal h(n) is a heuristic • Analysis • Greed tends to work quite well (despite being one of the seven deadly sins) • But, it doesn’t always find the shortest path • Susceptible to false starts • May go down an infinite path with no way to reach goal • How to ensure you’ll find the best solution?

17. A* • Can we apply the ideas of Dijkstra’s algorithm? • Pay attention to total path length, not just distance to the goal f(n) = g(n) + h(n) g(n) = distance traveled so far h(n) = estimated remaining distance (heuristic) • A*: do a DFS-like search with lowest f(n) first • Does this guarantee an optimal solution?

18. Optimality of A* • Suppose h(n) never overestimates(such heuristics are called admissible) • Note that f(n) always increases as search progresses • A* is complete and optimal (though often slower than best-first search) • The first limitation you are likely to run into with A* search: not enough RAM in your computer…

19. Heuristics for the 8-puzzle • What would a good, admissible heuristic be for the 8-puzzle? • h1: number of tiles out of place • h2: total distance of squares from destinations

20. Results of A* • Consider solving the 8-puzzle by search, using the following algorithms • DFS • BFS • IDS (iterative deepening search): like staged DFS. • A* with heuristic h1 • A* with heuristic h2 • Will each be able to find the shortest solution? • Which one will find it most quickly? • Which ones will use lots of memory?

22. AI and Personhood • AI proponents: • a machine as complex as a brain would be as intelligent as a person • maybe it would be a person. • Hidden assumptions: • intelligence: I/O, storage, and processing capabilities • the brain: a machine whose function can be duplicated by other machines (and function is what matters) • a person: an intelligent hunk of meat

23. What makes a person? • Is there anything to being a person besides “intelligence”? • Consciousness: is it an ‘epiphenomenon’ – or can it affect the body? • Will: do we make real choices, or are they determined by the laws of physics? • Affections: is there a ‘love’ algorithm? • Spirit: is there a human capability to know God beyond the five sense? • Moral responsibility: what are you doing when you kick your computer – punishment?

24. What are these views called? • “all the world (including the brain and mind) operate according to physical laws” • Materialism [or metaphysical materialism] • “There is a part of the mind (or soul or spirit) that is outside of nature, exempt from physical laws” • Dualism [or Cartesian dualism] • “The mind is the program running on the ‘wet-ware’ of the brain” • Functionalism [or non-reductive materialism]

25. Non-Reductive Materialism • Characteristics • there is no non-physical part of a person • mental processes can be localized in the brain • consciousness, will, etc. are real, but they are an ‘emergent property’ of brain function • Questions • How could there be a real will or moral responsibility? • Where is the intensionality or meaning? • What then can a verse like Matt. 10:28 mean? [Do not be afraid of those who kill the body but cannot kill the soul.] • What about the existence of angels, God if there is no second substance? • What of church history and doctrine?

26. Cartesian Dualism • Characteristics • The soul is a second substance, created by God, like the Angels • The mind is a faculty of the soul, and it can affect the body • Whatever the brain does, it is not the mind • Questions • A second substance is messy… • Where does this soul come from? How does it affect the body without breaking the laws of nature? • It seems that current research is localizing more and more mental processes in the brain… • What does this do to the science of AI?