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Slide 1 - Artificial Intelligence Fall 2008 Frank Hadlock
Slide 2 - Definitions of AI The study of representation and search through which intelligent activity can be enacted on a mechanical device. The study of problems at which human beings are currently more adept than computers at solving and the translation and improvement of human solutions into forms which can be implemented on a computer.
Slide 3 - Physical symbol system hypothesis The physical symbol system hypothesis (PSSH), first formulated by Newell and Simon in their Turing Award paper,1 states that “a physical symbol system [such as a digital computer, for example] has the necessary and sufficient means for intelligent action.” The hypothesis implies that computers, when we provide them with the appropriate symbol-processing programs, will be capable of intelligent action. It also implies, as Newell and Simon wrote, that “the symbolic behavior of man arises because he has the characteristics of a physical symbol system.”
Slide 4 - History Graph theory & state space representation (Euler) Boolean algebra – propositional calculus (Boole) Predicate calculus – (Frege) Descartes Discourse Turing’s Test Physical Symbol System Hypothesis Connectionism
Slide 5 - Discourse - Descartes If there were machines which bore a resemblance to our bodies and imitated our actions as closely as possible for all practical purposes, we should still have two very certain means of recognizing that they were not real men. The first is that they could never use words, or put together signs, as we do in order to declare our thoughts to others. For we can certainly conceive of a machine so constructed that it utters words, and even utters words that correspond to bodily actions causing a change in its organs. … But it is not conceivable that such a machine should produce different arrangements of words so as to give an appropriately meaningful answer to whatever is said in its presence, as the dullest of men can do. Secondly, even though some machines might do some things as well as we do them, or perhaps even better, they would inevitably fail in others, which would reveal that they are acting not from understanding, but only from the disposition of their organs. For whereas reason is a universal instrument, which can be used in all kinds of situations, these organs need some particular action; hence it is for all practical purposes impossible for a machine to have enough different organs to make it act in all the contingencies of life in the way in which our reason makes us act. (Translation by Robert Stoothoff)
Slide 6 - Turing Test The Turing test is a proposal for a test of a machine's ability to demonstrate intelligence. Described by Alan Turing in the 1950 paper "Computing Machinery and Intelligence," it proceeds as follows: a human judge engages in a natural language conversation with one human and one machine, each of which try to appear human; if the judge cannot reliably tell which is which, then the machine is said to pass the test. In order to test the machine's intelligence rather than its ability to render words into audio, the conversation is limited to a text-only channel such as a computer keyboard and screen (Turing originally suggested a teletype machine, one of the few text-only communication systems available in 1950).
Slide 7 - AI Application Areas Game Playing Automated Reasoning Expert Systems Natural Language Understanding Modeling Human Performance Planning and Robotics Languages for AI (Clips, Lisp and Prolog) Machine Learning Neural nets and Genetic Algorithms Intelligent Agents
Slide 8 - Game Playing and State Space Search
Slide 9 - Graph theory: The city of Königsberg The city is divided by a river. There are two islands at the river. The first island is connected by two bridges to both riverbanks and is also connected by a bridge to the other island. The second island two bridges each connecting to one riverbank. Question: Is there a walk around the city that crosses each bridge exactly once? Swiss mathematician Leonhard Euler invented graph theory to solve this problem.
Slide 10 - The city of Königsberg
Slide 11 - Graph of the Königsberg bridge system
Slide 12 - Euler Circuits A graph has an Euler circuit iff it is connected and every vertex is of even degree. Necessity – Euler circuit enters a vertex each time on a new edge and leaves the vertex on a new edge. So vertex has degree 2 * number of times on circuit Sufficiency – Pick starting vertex and traverse graph, each time picking new edge. Can only be blocked at start. Either have Euler circuit or can pick vertex with unused edge on circuit and build subtour starting with it. Splice subtour in. Eventually will have used all edges once.
Slide 13 - State space search Represented by a four-tuple [N,A,S,GD], where: N is the problem space A is the set of arcs (or links) between nodes. These correspond to the operators. S is a nonempty subset of N. It represents the start state(s) of the problem.
Slide 14 - State Space Search continued GD is a nonempty subset of N. It represents the goal state(s) of the problem. The states in GD are described using either: a measurable property of the states a property of the path developed in the search (a solution path is a path from node S to a node in GD )
Slide 15 - The 8-puzzle problem as state space search states: possible board positions operators: one for sliding each square in each of four directions,or, better, one for moving the blank square in each of four directions initial state: some given board position goal state: some given board position Note: the “solution” is not interesting here, we need the path.
Slide 16 - Eight Puzzle
Slide 17 - State space of the 8-puzzle generated by “move blank” operations
Slide 18 - Traveling salesperson problem as state space search The salesperson has n cities to visit and must then return home. Find the shortest path to travel. state space: operators: initial state: goal state:
Slide 19 - Automated Reasoning and Theorem Proving Logic systems began with Propositional Calculus in which declarative statements with a truth value of true or false are represented by P,Q,R, etc and combined with logic operators Or, And, Not, If. A sentence such as “Bill must take CSC 2020” is represented by letter P and is true or false. Propositional Calculus was extended to Predicate Calculus by adding Predicates (relations), variables, and quantifiers (For All and There Exists). A sentence such as “Every CS major must take CSC 2020” is represented by “(For All X)( CSMajor(X)  MustTake( CSC2020 ))” Given some facts expressed in either Propositional or Predicate Calculus, new facts or knowledge is inferred by inference rules such as modus ponens or resolution. If the computer can find a path from given facts to a new theorem, the path corresponds to a proof and finding such a path constitutes an example of artificial intelligence
Slide 20 - Propositional Logic A declarative statement such as “Bill is a CS student” has a truth value of T or F and is denoted by P (a truth variable) Propositions may be combined with logical operators and the composite statement has value as shown below. P  Q is true if either P or Q are true and false if both are false P  Q is true if both P and Q are true and false if either is false. ¬ P is true if P is false and false if P is true P  Q is true if P and Q have the same truth value and false if their values differ P  Q is false if P is true and Q is false and true otherwise. A tautology is always true. P  Q  ¬ P  Q is a tautology. P  (Q  R)  (P  Q)  (P  R) is a tautology.
Slide 21 - Rules of Inference P , P  Q then Q - modus ponens ¬ Q, P  Q then ¬ P - modus tollens
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Slide 24 - Cognitive AlgebraTutors Algebra class may be less difficult and a bit more fun these days, thanks to research on how human cognition works. Developed over two decades by psychologist John Anderson, the Adaptive Character of Thought (ACT-R) theory is a framework for understanding how we think about and attack problems, including math equations. The theory reflects our understanding o human cognition based on numerous facts derived from psychological experiments. ACT-R suggests that complex cognition arises from an interaction of procedural and declarative knowledge. Declarative knowledge is a fairly direct encoding of facts (such as Washington, DC is the capital of the United States, 5 + 3 =8); procedural knowledge is a fairly direct encoding of how we do things (such how to drive or how to perform addition). According to the ACT-R theory, the power of human cognition depends on how people combine these two types of knowledge. Significance The ACT-R theory provides insights into how students learn new skills and concepts, and, in doing so allows teachers to see where students may need extra practice to master the new work. Practical Application Dr. Anderson and colleagues at Carnegie Mellon University have used this research to develop cognitive tutors, computer-tutoring programs that incorporate the ACT-R theory in the teaching of algebra, geometry and integrated math. The tutors are based on cognitive models that take the form of computer simulations that are capable of solving the types of problems that students are asked to solve. The tutors incorporate the declarative and procedural knowledge imbedded in the instruction and monitor students’ problem solving to determine what the students know and don’t know. This allows instruction to be directed at what still needs to be mastered and helps insure that students’ learning time is spent in a more efficient manner. Students work on a concept until it is fully understood. Students who are having conceptual problems will be drilled on in that area, while those who have mastered the concept move on to other areas. The most widely used cognitive tutor program – now known as Carnegie Learning’s Cognitive Tutor - combines software-based, individualized computer lessons with collaborative, real-world problem-solving activities. The program now serves more than 150,000 students in most of the nation’s largest school districts. Field studies have shown dramatic student achievement gains where the program is in use. In 2003, the U.S. Department of Defense Schools awarded a contract that will use Cognitive Tutor mathematics curricula in its 224 public schools in 21 districts located in 14 foreign countries, seven states, Guam and Puerto Rico. These schools have approximately 8,800 teachers serving 106,000 students. Cited Research Anderson, J. R. (1983). The architecture of cognition. Cambridge: MA: Harvard University Press. Anderson, J. R. (1993). Rules of the Mind. Hillsdale, NJ: Erlbaum.
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Slide 26 - Fact List (deftemplate pay (slot hours)(slot rate)) (deffacts payroll ( pay (hours 44)(rate 8)) (status incomplete) )
Slide 27 - Fact List Rule List (defrule calculate_basic ?p <- (pay (hours ?h)(rate ?r)) (test (<= ?h 40)) => (assert (basic_pay (* ?h ?r))) (retract ?p) )
Slide 28 - Rule List Rule List (defrule calculate_basic ?p <- (pay (hours ?h)(rate ?r)) (test (<= ?h 40)) => (assert (basic_pay (* ?h ?r))) (retract ?p) ) (defrule calculate_overtime (pay (hours ?h)(rate ?r)) (test (> ?h 40)) (status incomplete) => (assert (overtime (* (- ?h 40) (* ?r 1.5)))) ) (defrule calculate_regular (pay (hours ?h)(rate ?r)) (status incomplete) (test (> ?h 40)) => (assert (regular (* 40 ?r) )) ) (defrule calculate_adjustedgross (regular ?r) (overtime ?o) (status incomplete) => (assert (adjusted_gross (+ ?r ?o))) (assert (status done)) ) (deftemplate pay (slot hours)(slot rate)) (deffacts payroll ( pay (hours 44)(rate 8)) (status incomplete) )
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Slide 30 - Representation and Search Representation of Problem Information Propositional & Predicate Logic Semantic networks State Space set of problem states along with transitions between states and a set of start states and goal states. a path from start to goal is a solution Search Techniques for finding a solution
Slide 31 - Eight Puzzle Representation – The squares of the eight puzzle can be represented by integers 1 .. 8 and 9 represents empty square. A state of the puzzle is a permutation of 1..9 where 1st three represent top row, 2nd three represent middle row, and 3rd three represent bottom row.
Slide 32 - Eight puzzle transitions An eight puzzle transition consists of moving a square numbered 1..8 into the adjacent vacant square which can only be done if it is adjacent to the numbered square. Representation of a board configuration is a permutation of 1..9 where 9 represents vacant square. Example – 132496758 represents 1st row 132, 2nd row 4 blnk 6, 3rd row 748. Since the blank is in the middle position, 3 can be moved down, or 4 to the right, or 6 to the left, or 5 moved up. These transitions make 132496758 have neighbors 192436758, 132946758, 132469758, and 132456798.
Slide 33 - Knowledge Representation Essential to artificial intelligence are methods of representing knowledge. Besides propositional and predicate logic, a number of other methods have been developed, including: Semantic Networks Conceptual Dependencies Scripts Frames
Slide 34 - Semantic Networks Models meaning of language: Nodes correspond to word concepts Arcs are labeled with a property name or relationship and link a node (word concept) with another (value of property). Quillian (1967) introduced semantic networks while others (Simmons -1973, Brachman-1979, Schank-1979) have extended the model.
Slide 35 - Semantic NetworksStandardization of Relationships Standardization of relationships for representing knowledge expressed in language focuses on case relations between verbs and nouns in sentence (Fillmore ’68, Simmons ’73) Prepositions or articles indicate relationship between verb and noun : Agent : entity performing the action Object : entity acted upon Instrument : entity used in performing the action Etc.
Slide 36 - Conceptual DependenciesSet of Primitive Actions Standardization of relations led to axiomatic approach to build semantic model for representing meaning of language Each Action is assumed to reduce to one or more of the primitive ACTs
Slide 37 - Building Complex Conceptual Dependencies
Slide 38 - Scripts Scripts formalize stereotyped sequences of events. A script for a restaurant differs from one for a “fast food” model. The components of a script are Entry conditions which must be true for script to be activated Termination conditions which are true when script is terminated. Props or object which support the script. The script for a restaurant would include table and cash register props. Roles are the actions that individual participants must perform. The waiter takes orders, the customer eats and pays bill. Scenes break the script into subsequences which Are sequential in occurerence Provide alternatives (if condition A then Scene1 elsce Scene2)
Slide 39 - Frames Frames formalize stereotyped entities and actions. Frames have labeled slots with slot contents an object or action and slot labels are the role played by the slot filler in relation to the central entity of action. A frame is like a record that contains information relevant to stereotyped action or entity: Frame Identification Relationship to other frames (part-of, caused-by) Slots Label indicating relationship to central slot Requirements for slot filler Procedural information to construct or manipulate slot contents Default Contents Slot contents
Slide 40 - Frame Examples
Slide 41 - Conceptual GraphsA Network Language A conceptual graph is a refinement of semantic networks. A conceptual graph is bipartite with one class of nodes representing word concepts and the other class of nodes representing relations. Arcs go from concept class nodes to relation class nodes and vise vesa.
Slide 42 - Conceptual Graph Examples bird flies dog color brown child parents mother father mary agent give object book recipient john