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5,6exampleslide

# 5,6exampleslide - SOME PROBLEMS chapters 5,6 Reminder We...

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SOME PROBLEMS: chapters 5,6 Reminder: We define H semantics operations and as follows a b = max { a, b } , a b = min { a, b } . The Truth Tables for Implication and Nega- tion are: H-Implication F T F T T T F T T T F T H Negation ¬ F T T F F 1

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QUESTION 1 We know that v : V AR -→ { F, , T } is such that v * (( a b ) ( a c )) = under H semantics. evaluate v * ((( b a ) ( a ⇒ ¬ c )) ( a b )). 2
Solution : v * (( a b ) ( a c )) = under H semantics if and only if (we use shorthand notation) ( a b ) = T and ( a c ) = if and only if a = T, b = T and ( T c ) = if and only i f c = . I.e. we have that v * (( a b ) ( a c )) = iff a = T, b = T, c = . Now we can we evaluate v * ((( b a ) ( a ⇒ ¬ c )) ( a b )) as follows (in short- hand notation). v * ((( b a ) ( a ⇒ ¬ c )) ( a b )) = ((( T T ) ( T ⇒ ¬ ⊥ )) ( T T )) = (( T ( T F )) T ) = T . 3

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We define a 4 valued ˆL 4 logic semantics as follows. The language is L = L , , , ∩} .
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5,6exampleslide - SOME PROBLEMS chapters 5,6 Reminder We...

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