Knowledge-based systems

Transcription

1 CS 750 Foundations of I Lecture 6 Knowledge-based systems Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square dministration announcements Midterm: Thursda October 6, 07 In-class Closed book What does it cover? ll material covered by the end of lecture toda October 4, 07 CS 57 Intro to I

2 Knowledge-based system Knowledge base Inference engine Knowledge base: set of sentences that describe the world in some formal representational language e.g. first-order logic Domain specific knowledge Inference engine: set of procedures that work upon the representational language and can infer new facts or answer K queries e.g. resolution algorithm, forward chaining Domain independent utomated reasoning systems Eamples and main differences: Theorem provers Prove sentences in the first-order logic. Use inference rules, resolution rule and resolution refutation. Deductive retrieval systems Systems based on rules Ks in Horn form Prove theorems or infer new assertions forward, backward chaining Production systems Systems based on rules with actions in antecedents Forward chaining mode of operation Semantic networks Graphical representation of the world, objects are nodes in the graphs, relations are various links

3 Production systems ased on rules, but different from Ks in the Horn form Knowledge base is divided into: Rule base includes rules Working memory includes facts special type of if then rule p p pn a, a,, a k ntecedent: a conjunction of literals facts, statements in predicate logic Consequent: a conjunction of actions. n action can: DD the fact to the K working memory REMOVE the fact from the K consistent with logic? QUERY the user, etc Production systems ased on rules, but different from Ks in the Horn form Knowledge base is divided into: Rule base includes rules Working memory includes facts special type of if then rule p p pn a, a,, a k ntecedent: a conjunction of literals facts, statements in predicate logic Consequent: a conjunction of actions. n action can: DD the fact to the K working memory REMOVE the fact from the K!!! Different from logic QUERY the user, etc 3

4 Production systems Use forward chaining to do reasoning: If the antecedent of the rule is satisfied rule is said to be active then its consequent can be eecuted it is fired Problem: Two or more rules are active at the same time. Which one to eecute net? R7 R05 Conditions R7 Conditions R05 ctions R7 ctions R05? Strategy for selecting the rule to be fired from among possible candidates is called conflict resolution Production systems Why is conflict resolution important? Or, why do we care about the order? ssume that we have two rules and the preconditions of both are satisfied: R: C y add D R: E z delete What can happen if rules are triggered in different order? 4

5 Production systems Why is conflict resolution important? Or, Why do we care about the order? ssume that we have two rules and the preconditions of both are satisfied: R: R: C y add D E z delete What can happen if rules are triggered in different order? If R goes first, R condition is still satisfied and we infer D If R goes first we may never infer D Production systems Problems with production systems: dditions and Deletions can change a set of active rules; If a rule contains variables, testing all instances in which the rule is active may require a large number of unifications. Conditions of many rules may overlap, thus requiring to repeat the same unifications multiple times. Solution: Rete algorithm gives more efficient solution for managing a set of active rules and performing unifications Implemented in the system OPS-5 used to implement XCON an epert system for configuration of DEC computers 5

6 Rete algorithm ssume a set of rules: C y add D y D add E E z delete nd facts:,,, 3, 4, C5 Rete: Compiles the rules to a network that merges conditions of multiple rules together avoid repeats Propagates valid unifications Reevaluates only changed conditions Rete algorithm. Network. Rules: Facts: C y add D y D add E E z delete,,, 3, 4, C5 6

7 7 Rete algorithm. Network. D add y C E add D y delete z E 5 4, 3,,,, C Rules: Facts: Rete algorithm. Network. D add y C E add D y delete z E 5, 4, 3,,,, D C Rules: Facts: D E

8 Conflict resolution strategies Problem: Two or more rules are active at the same time. Which one to eecute net? Solutions: No duplication do not eecute the same rule twice Recency. Rules referring to facts newly added to the working memory take precedence Specificity. Rules that are more specific are preferred. Priority levels. Define priority of rules, actions based on epert opinion. Have multiple priority levels such that the higher priority rules fire first. Semantic network systems Knowledge about the world described in terms of graphs. Nodes correspond to: Concepts or objects in the domain. Links to relations. Three kinds: Subset links isa, part-of links Member links instance links Function links. Inheritance relation links Can be transformed to the first-order logic language Graphical representation is often easier to work with better overall view on individual concepts and relations 8

9 Semantic network. Eample. Water Transports on Ship isa isa is-part is-part Ocean liner Oil tanker Engine Hull is-part member member is-part Swimming pool Queen Mary Eon Valdez oiler Inferred properties: Queen Mary is a ship Queen Mary has a boiler CS 57 Intro to I Lecture 6b Modeling time and actions Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square 9

10 Representation of actions, situations, events Propositional and first order logic are monotonic Once something is true it cannot become false ut, the world is dynamic: What is true now may not be true tomorrow Changes in the world may be triggered by our activities Problems: How to represent the change in the FOL? How to represent actions we can use to change the world? Planning Planning problem: find a sequence of actions that achieves some goal an instance of a search problem the state description is typically very comple and relies on a logic-based representation Methods for modeling and solving planning problems: State space search Situation calculus based on FOL STRIPS state-space search algorithm based on restricted FOL Partial-order planning algorithms 0

11 Situation calculus Provides a framework for representing change, actions and for reasoning about them Situation calculus based on the first-order logic, a situation variable models possible states of the world properties and relations depend on different world states situations action objects model activities Inference: inference methods developed for FOL to do the reasoning Situation calculus Logic for reasoning about changes in the state of the world The world dynamics is described by: Sequences of situations of the current state Changes from one situation to another are caused by actions The situation calculus allows us to: Describe the initial state and the goal state uild the K that describes the effect of actions operators Prove that the K and the initial state can lead to the goal state etracts a plan sequence of actions as side-effect of the proof

12 Situation calculus The language is based on the First-order logic plus: Special variables: s,a objects of type situation and action ction functions: return actions action objects. E.g. Move, TLE, represents a move action Move,z represents an action schema Special function symbols of type situation s 0 initial situation DOa,s represents the situation that is obtained after performing action a in situation s Situation-dependent predicates, functions also called fluents Relation: On,s object is on object y in situation s; Function: bove,s object that is above in situation s. Situation calculus. locks world eample. C C Initial state On, s 0 On, s 0 On s 0 Clear, s 0 Clear, s 0 Clear s 0 Clear s 0 Goal Find a state situation s, such that On,, s On, s On s

13 Knowledge base: ioms Knowledge base is needed to support the reasoning: Must represent changes in the world due to actions. Two types of aioms: Effect aioms changes in situations that result from actions Frame aioms things preserved from the previous situation Eample: blocks world with On, Clear predicates Move actions locks world eample. Effect aioms. Effect aioms: represent the changes after the action is eecuted Moving from y to z. MOVE, z Effect of move changes on On relations On, s Clear, s Clear z, s On, z, DO MOVE, z, s On, s Clear, s Clear z, s On, DO MOVE, z, s Effect of move changes on Clear relations On, s Clear, s Clear z, s Clear DO MOVE, z, s On, s Clear, s Clear z, s z Table Clear z, DO MOVE, z, s 3

14 locks world eample. Frame aioms. Frame aioms. Represent relations/properties that remain unchanged by the eecuted action Eplicitly move the relations to the net situation after the action On relations: On u, v, s u v y On u, v, DO MOVE, z, s Clear relations: Clear u, s u z Clear u, DO MOVE, z, s Planning in situation calculus Planning problem: find a sequence of actions that lead to the goal Planning in situation calculus is converted to the theorem proving problem Goal state: s On,, s On, s On s Possible inference approaches: Inference rule approach Conversion to ST Plan solution is a byproduct of theorem proving Eample: blocks world 4

15 Planning in the blocks world. C C Initial state s0 s 0 On, s0 On, s0 On s 0 s Clear, s0 Clear, s0 Clear s 0 Clear s0 ction: MOVE, C s DO MOVE, s0 On, s Clear, s On, s On, s Clear, s On s Clear s Clear s Planning in the blocks world. C C C Initial state s0 s s s DO MOVE, s0 On, s On, s Clear, s On, s Clear, s On s Clear s Clear s ction: MOVE, s DO MOVE,, s DO MOVE,, DO MOVE, s 0 On,, s On, s On, s On, s On s Clear, s Clear Clear Clear, s s s 5

16 Planning in the blocks world. C C C Initial state s0 s s s DO MOVE, s0 On, s On, s Clear, s On, s Clear, s On s Clear s Clear s ction: MOVE, s DO MOVE,, s DO MOVE, Table Satisfies,, DOthe MOVE goal, s 0 On,, s On, s On, s On, s On s Clear, s Clear Clear Clear, s s s Planning in the blocks world. C C C Initial state s0 s s s DO MOVE, s0 On, s On, s Clear, s Clear s On, s Clear, s On s Clear s DO functions capture ction: MOVE, the plan s DO MOVE,, s DO MOVE,, DO MOVE, s 0 On,, s On, s On, s On, s On s Clear, s Clear Clear Clear, s s s 6

17 Situation calculus: problems Frame problem refers to: The need to represent a large number of frame aioms Solution: combine positive and negative effects in one rule On u, v, DO MOVE, z, s u v y On u, v, s u v z On, s Clear, s Clear z, s Inferential frame problem: We still need to derive properties that remain unchanged Other problems: Qualification problem enumeration of all possibilities under which an action holds Ramification problem enumeration of all inferences that follow from some facts 7