Foundations of Artificial Intelligence. Reasoning

Transcription

1 Foundations of Artificial Intelligence Reasoning

2 Uncertainty and Reasoning - What is knowledge? - How do we search through knowledge? - How do we get knowledge? - How do we represent knowledge? - How do deal with vague knowledge? How do we reason through knowledge?

3 Objectives Reasoning Introduce the way AI systems reason through knowledge. Give an understanding of Modens Ponens Diagrammatic Substitution Backward Chaining Forward Chaining Students should gain the ability to apply and use diagrammatic substitution to solve problems. Students should be able to follow the chain of inference through a knowledge base using both backward and forward chaining.

4 If I tell you: All boys have a mother and that: "John is a boy" What can you tell me about John?

5 If I tell you: All boys have a mother and that: "John is a boy" You are able to figure out that: "John has a mother without being explicitly told this fact.

6 All boys have a mother "John is a boy" "John has a mother To know that John is a boy or that all boys have mothers merely requires retrieval of previously stored facts. To know that John has a mother requires the ability to reason from the available facts.

7 When we require any knowledge system to do something it has not been explicitly told how to do it must reason. The system must figure out what it needs to know from what it already knows.

8 We have just seen an example of reasoning or drawing inferences. For example if we know: Robins are birds. All birds have wings. Then if we ask: Do robins have wings? Some reasoning (albeit very simple) has to go on answer the question.

9 A good knowledge representation scheme has to allow easy, natural and plausible reasoning. A knowledge based system is an essentially declarative system. The reasoning part of a knowledge based system is the inference engine.

10 There are problems facing the inference engine, such as: A knowledge system must have a way to decide where to start. Rules and facts reside in a static knowledge base. There must be a way for the reasoning process to begin. The inference engine must resolve conflicts that occur when alternative lines of reasoning emerge. It could be, for example, that the system reaches a point at which four or more rules are ready to fire. The inference engine must choose which rule to examine next.

11 This is the simplest and most fundamental form of inference; it was known and described by Aristotle, and stood us in good stead for over 2000 years. It is the rule of modus ponens. The schema is simply : from and infer if p then q p q

12 if it is raining then the ground is wet if height of X > height of Y then X is taller than Y where X and Y are variables, and the database has the following items: it is raining height of Tom = 6 height of Tim = 5 RULES the ground is wet Tom is taller than Tim

13 Substitution processes, are extremely important. Sometimes mere substitution immediately reveals the truth of the theorem without our needing to go through the formality of applying a complex resolution process. A formal way of representing this reasoning is diagrammatic substitution. Lets consider two facts and one implication, from which we would like to be able to prove a third fact.

14 TUTORIAL EXAMPLE A particular planning schedule is reliant on three tasks Task A, Task B and Task C. We know three facts about the tasks : Fact 1 :- Task A is dependant on Task B Fact 2 :- Task B is dependant on Task C Fact 3 :- Task C is behind schedule We know two implications about planning scheduling : Implication 1 If X is dependant on Y and Y is dependant on Z then X is dependant on Z. Implication 2 If X is dependant on Y and Y is behind schedule then X is behind schedule. Use diagrammatic substitution to show that Task A is behind schedule.

15 TUTORIAL EXAMPLE A particular planning schedule is reliant on three tasks Task A, Task B and Task C. We know three facts about the tasks : Fact 1 : D (A, B) (A is dependant on B) Fact 2 : D (B, C) (B is dependant on C) Fact 3 : BS (C) (C is behind schedule) We know two implications about planning scheduling : Implication 1 : (x) : (y) : (z) : D (x, y) D (y, z) D (x, z) Implication 2 : (x) : (y) : D (x, y) BS (y) BS (x) Use diagrammatic substitution to show that BS (A)

16 D (x, y) D (y, z) D (x, z) TUTORIAL EXAMPLE x = A y = B D (A, B) Fact 1 D (B, z) D (A, z) z = C D (B, C) Fact 2 D (A, C) Conclusion 1

17 TUTORIAL EXAMPLE D (x, y) BS (y) BS (x) x = A y = C D (A, C) Conclusion 1 BS (C) Fact 3 BS (A) Conclusion 2

18 The rule of modus ponens, however, does not tell us how to set about solving a problem. It does not tell us where to start and how to proceed. Apart from a rule of inference, we need in addition some principle of strategy.

19 There are two strategies that have also long been employed in logic and mathematics: We can work forward from the given to the conclusion. This mode of proceeding answers the question: What can we conclude from the given data? Or we can work backwards (as long as we know where we want to end up, of course) from the hypothesis to the data supporting it. This mode answers the question: Can we prove the hypothesis from the given data?

20 Four factors influence the question of whether it is better to reason forward or backward: Are there more possible start states or goal states? In which direction is the branching factor greater? Will the program be asked to justify its reasoning process to a user? What kind of event is going to trigger a problemsolving episode?

21 Forward Chaining Lets look at some example demons : when it rained yesterday then ground is wet when excavation material is earth and ground is wet then ground condition is muddy The following facts are known : Note : Forward chaining rules are called demons Rules and demons are fired when they are used it rained yesterday excavation material is earth

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23 Backward Chaining Lets look at some example rules : if it rained yesterday then ground is wet if excavation material is earth and ground is wet then ground condition is muddy The following facts are known : it rained yesterday excavation material is earth Reasoning

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25 Take the following rules : if temperature > 60 then furnace is hot Reasoning Tutorial if product is milled steel and furnace is hot then temperature dial setting is number 3 The following facts are known : temperature = 90 product is milled steel Follow the logic of an inference engine on these rules with both a forward and backward chaining regime.

26 Hybrid Systems The differing strengths and weaknesses of forward and backward chaining have raised interest in efforts to integrate them into some sort of bi-directional search (goal-directed and data-driven) combining the best of both worlds.

27 Summary Introduced the way AI systems reason through knowledge. Given an understanding of Modens Ponens Diagrammatic Substitution Backward Chaining Forward Chaining