Inexact reasoning

Knowledge & Inexact Reasoning ,[object Object],[object Object],[object Object],[object Object],[object Object]

Inexact Reasoning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Forms of Inexact Knowledge ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Inexact Knowledge - Example ,[object Object],default - A wants to take a bus belief, (un)certainty - it's the neighbor B probability, default, uncertainty - the neighbor goes home by car default - A wants to get a lift default - A wants to go home Q: Which forms of inexact knowledge and reasoning are involved here?

Examples of Inexact Knowledge ,[object Object],Fuzzy - a few hundred yards define a mapping from " #hundreds " to ' few ', ' many ', ... not uncertain or incomplete but graded, vague Probabilistic - the neighbor usually goes by car probability based on measure of how often he takes car; calculates always p(F) = 1 - p( ¬F) Belief - it's his next-door neighbor B "reasoned assumption", assumed to be true Default - A wants to take a bus assumption based on commonsense knowledge

Dealing with Inexact Knowledge ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Uncertainty and Rules ,[object Object],[object Object],[object Object],[object Object],[object Object]

Figure 5.1 Major Uncertainties in Rule-Based Expert Systems

Figure 5.2 Uncertainties in Individual Rules

Figure 5.3 Uncertainty Associated with the Compatibilities of Rules

Figure 5.4 Uncertainty Associated with Conflict Resolution

Goal of Knowledge Engineer ,[object Object],[object Object],[object Object]

Verification vs. Validation ,[object Object],[object Object],[object Object],[object Object]

Ad Hoc Methods ,[object Object],[object Object],[object Object]

Sources of Uncertainty ,[object Object],[object Object]

Uncertainty in Conflict Resolution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Uncertainty ,[object Object],[object Object],[object Object]

Certainty Factors ,[object Object]

Difficulties with Bayesian Method ,[object Object],[object Object],[object Object]

Belief and Disbelief ,[object Object],[object Object],[object Object],[object Object]

Belief and Disbelief ,[object Object],[object Object],[object Object]

Likelihood of Belief / Disbelief ,[object Object],[object Object],[object Object]

Measures of Belief and Disbelief ,[object Object],[object Object],[object Object],[object Object]

Certainty Factor Values ,[object Object],[object Object],[object Object],[object Object]

Threshold Values ,[object Object],[object Object],[object Object],[object Object]

Difficulties with Certainty Factors ,[object Object],[object Object],[object Object]

Dempster-Shafer Theory ,[object Object],[object Object]

Dempster-Shafer ,[object Object],[object Object]

Dempster-Shafer ,[object Object],[object Object],[object Object],[object Object]

Dempster-Shafer ,[object Object],[object Object],[object Object],[object Object],[object Object]

Dempster-Shafer ,[object Object],[object Object],[object Object]

Dempster-Shafer ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Approximate Reasoning ,[object Object],[object Object],[object Object]

Fuzzy Sets and Natural Language ,[object Object],[object Object],[object Object],[object Object],[object Object]

Fuzzy Set Operations ,[object Object],[object Object]

Fuzzy Set Operations Set equality Set Complement Set Containment Proper Subset Set Union Set Intersection Set Product Power of a Set Probabilistic Sum Bounded Sum Bounded Product Bounded Difference Concentration Dilation Intensification Normalization

Fuzzy Relations ,[object Object],[object Object],[object Object],[object Object]

Fuzzy Relations ,[object Object],[object Object],[object Object]

Table 5.7 Some Applications of Fuzzy Theory

Table 5.8 Some Fuzzy Terms of Natural Language

Linguistic Variables ,[object Object],[object Object],[object Object]

Extension Principle ,[object Object],[object Object],[object Object]

Fuzzy Logic ,[object Object],[object Object]

Possibility and Probability and Fuzzy Logic ,[object Object],[object Object]

Translation Rules ,[object Object],[object Object],[object Object],[object Object],[object Object]

State of Uncertainty Commercial Applications ,[object Object],[object Object],[object Object],[object Object],[object Object]

Summary ,[object Object],[object Object],[object Object],[object Object]

Summary ,[object Object],[object Object]

Inexact reasoning

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Inexact reasoning