BAp

Generally, if we substitute “BAp” for p in the traditional definitional scheme's equivalences, we get:

Deontic Logic McNamara, Paul 2006

"Apply A to p and then apply B to that result." p '= B (Ap) = (BA) p = Cp Several translations composted to one Translations still left out ... p' = B (Ap + t) = BAp + Bt = Cp + u 27 27

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Composition Matrix multiplication composites matrices p '= BAp "Apply A to p and then apply B to that result." p' = B (Ap) = (BA) p = Cp Several translations composted to one Translations still left out ... p '= B (Ap + t) = BAp + Bt = Cp + u 27 27

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Slide 14: Composition Matrix multiplication composites matrices p '= BAp

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(The second clause is implied by the first) d) BA~p & ~BAp.

Deontic Logic McNamara, Paul 2006

BAp †’ p (BA-T) (if an agent brings about p, then p holds ” “success” clause), and the schema,

Deontic Logic McNamara, Paul 2006