Predicate Calculus

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Knowledge Representation (KR)
Given the world
• Express the general facts or beliefs using a language
• Determine what else we should (not) believe
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Example
Given:
?“The red block is above the blue block”
?“The green block is above the red block” Infer:
?“The green block is above the blue block”
?“The blocks form a tower”
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A KR language needs to be
• expressive
• unambiguous
• flexible
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The inference procedures need to be
• Correct (sound)
• Complete
• Efficient
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Logic consists of
• A language which tells us how to build up sentences in the language (i.e., syntax), and and what the sentences mean (i.e., semantics)
• An inference procedure which tells us which sentences are valid inferences from other sentences
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Propositional logic
The symbols of propositional calculus are the propositional symbols: P, Q, R, S, … the truth symbols: true, false and connectives: ?, ?, ?, ?, ?
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Propositional Calculus Sentences
Every propositional symbol and truth symbol is a sentence. Examples: true, P, Q, R. The negation of a sentence is a sentence. Examples: ?P, ? false. The conjunction, or and, of two sentences is a sentence. Example: P ? ?P
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Propositional Calculus Sentences (cont’d)
The disjunction, or or, of two sentences is a sentence. Example: P ? ?P The implication of one sentence from another is a sentence. Example: P ? Q The equivalence of two sentences is a sentence. Example: P ? Q ? R Legal sentences are also called well-formed formulas or WFFs.