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## 15 Definitions (Ad)## IntroductionIn order to be able to formulate Peirce's rules precisely, we first need to give some definitions. The definitions will be accompanied by explanations and examples. ## Definitions## Negative contextA [Proposition: [Person: JohnTheBaptist]- - - - -[Christ: #] ] "John the Baptist is not the Christ" ## Outermost contextEvery graph must -- explicitly or implicitly -- be part of a knowledge base, and every
knowledge base has an ## Evenly enclosedA concept or conceptual graph is said to be For example: [Proposition: [Proposition: [Men: ]->(Attr)->[Mortal] ] "It is not the case that it is not the case that all men are mortal" "All men are mortal" here, the innermost graph, [Men: ]->(Attr)->[Mortal] is evenly enclosed because, going outwards towards the outermost context, we encounter an even number of negative contexts (in this case, 2). Here is another example: [Proposition: [Situation: [Person: John]<-(Agnt)<-[Act: Say]- ->(Thme)->[Proposition: [Person: #I]- - - -[Swindler] ] ] ] "It is not the case that there is the following situation: John said, 'I am not a swindler" "John never said, 'I am not a swindler" Here, the innermost graph: [Person: #I]- - - -[Swindler] is evenly enclosed because we encounter an even number (two)
negative contexts on our way outwards to the outermost context.
Notice that there is an extra context, "Situation" in between the
outer negative context ("Proposition") and the inner negative context
(also "Proposition"). Thus the predicate ## Oddly enclosedA concept or conceptual graph is said to be For example: [Situation: [Person: JohnTheBaptist]<-(Agnt)<-[Act: Say]- ->(Thme)->[Proposition: [Person: #I]- - - -[Christ: #] ] ] "There is this situation: John the baptist says, 'I am not the Christ'". Here, the innermost graph: [Person: #I]- - - -[Christ: #] is oddly enclosed because, on our way outwards to the outermost context, we meet an odd (one) number of negative contexts. Again, it is precisely the number of ## DominationIf a context y occurs nested in a context x, then x is said to
For example: [x: [y: [z] ] ] y dominates z, while x dominates both y and z. ## Double negationA double negation is two nested negative contexts of type Proposition, where one is directly nested inside the other: [Proposition: [Proposition: // Content ] ] If we draw a double negation around any conceptual graph, the effect is to leave the graph's meaning unchanged. This is because ((p)) is the same as p. (To see this, try to say, "It is not the case that I am not hungry" and derive the meaning, "I am hungry".) ## SummaryA concept c is said to be a A concept c is A concept x is said to A ## NextWith these definitions, we are ready to formulate Peirce's rules. Prev: Part IV: Peirce's rules (Ad)Up: Part IV: Peirce's rules (Ad)Next: 16 Peirce's rules of inference (Ad) |