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hallow knowledge structures – all knowledge is contained in nodes and links. ? Schema is a more plex knowledge structure than a semantic . ? In a schema, a node is like a record which may contain data, records, and/or pointers to nodes. Expert Systems: Principles and Programming, Fourth Edition 31 Frames ? One type of schema is a frame (or script – timeordered sequence of frames). ? Frames are useful for simulating monsense knowledge. ? Semantic s provide 2dimensional knowledge。 frames provide 3dimensional. ? Frames represent related knowledge about narrow subjects having much default knowledge. Expert Systems: Principles and Programming, Fourth Edition 32 Frames Continued ? A frame is a group of slots and fillers that defines a stereotypical object that is used to represent generic / specific knowledge. ? Commonsense knowledge is knowledge that is generally known. ? Prototypes are objects possessing all typical characteristics of whatever is being modeled. ? Problems with frames include allowing unrestrained alteration / cancellation of slots. Expert Systems: Principles and Programming, Fourth Edition 33 Logic and Sets ? Knowledge can also be represented by symbols of logic. ? Logic is the study of rules of exact reasoning – inferring conclusions from premises. ? Automated reasoning – logic programming in the context of expert systems. Expert Systems: Principles and Programming, Fourth Edition 34 Figure A Car Frame Expert Systems: Principles and Programming, Fourth Edition 35 Forms of Logic ? Earliest form of logic was based on the syllogism – developed by Aristotle. ? Syllogisms – have two premises that provide evidence to support a conclusion. ? Example: – Premise: All cats are climbers. – Premise: Garfield is a cat. – Conclusion: Garfield is a climber. Expert Systems: Principles and Programming, Fourth Edition 36 Venn Diagrams ? Venn diagrams can be used to represent knowledge. ? Universal set is the topic of discussion. ? Subsets, proper subsets, intersection, union , contained in, and plement are all familiar terms related to sets. ? An empty set (null set) has no elements. Expert Systems: Principles and Programming, Fourth Edition 37 Figure Venn Diagrams Expert Systems: Principles and Programming, Fourth Edition 38 Syllogism 三段論法 Premise: All men are mortal Premise: Socrates is a man Conclusion: Socrates is mortal Only the form is important. Premise: All X are Y Premise: Z is a X Conclusion: Z is a Y Expert Systems: Principles and Programming, Fourth Edition 39 Categorical Syllogism ? Syllogism: a valid deductive argument having two premises and a conclusion. major premise: All M are P minor premise: All S is M Conclusion: All S is P M middle term P major term S minor term Expert Systems: Principles and Programming, Fourth Edition 40 Categorical Statements Form Schema Meaning A All S is P universal affirmative E No S is P universal negative I Some S is P particular affirmative O Some S is not P particular negative Expert Systems: Principles and Programming, Fourth Edition 41 Mood AAA1 EAE1 IAI4 All M is P No M is P Some P is M All S is M All S is M All M is S All S is P No S is P Some S is P Figure 1 2 3 4 Major Premise M P P M M P P M Minor Premise S M S M M S M S Expert Systems: Principles and Programming, Fourth Edition 42 Propositional Logic ? Formal logic is concerned with syntax of statements, not semantics. ? Syllogism: ? All goons are loons. ? Zadok is a goon. ? Zadok is a loon. ? The words may be nonsense, but the form is correct – this is a “valid argument.” Expert Systems: Principles and Programming, Fourth Edition 43 Figure Intersecting Sets Expert Systems: Principles and