Possibilities of logically equivalent expressions

✍ Scribed by Harvey J. Greenberg

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 97 KB
• Volume: 86
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00191-1

✦ Synopsis

If A is logically equivalent to B, it is not necessary that #(A) = p(B). This technical note proves, however, that if A is in CNF, there exists some logically equivalent DNF, B, such that p(A) = #(B). © 1997 Elsevier Science B.V. Let #(P) denote the possibility of P being true, where 0 ~< p(P) ~< 1. Define the usual calculus [1, 2] #(~P) ---1 -p(P); p(P v Q) = max[#(P), p(Q)]; p(P ^ Q) = min[p(P), #(Q)].