I gained a great deal of knowledge during my college years, which is as it should be. In a Philosophy Logic class, I learned about truth tables and fell in love with them. Ludwig Wittgenstein is often credited with their invention. Ludwig himself was an interesting character. I read a great biography of the man years back, called Wittgenstein’s Poker. He is not a person one would want to share a dorm room with. But I digress…
Truth tables are used to determine the logical coherence of a statement. In formal argumentation, they are used to dissect a statement for truthfulness. Truth tables are a helpful exercise in software development as well. They use logical operators in combinations to determine the truth or falseness of a statement.
Subjecting each quantitative risk to the rigor of a truth table would be overkill for all but the most profound risks. However, retaining a truth table outlook on statements that will end up as part of your simulation will improve the overall quality of the risk assessment and increase the accuracy of your model.
Wikipedia has a great demonstrative:
Truth table for all binary logical operators
Here is a truth table giving definitions of all 16 of the possible truth functions of two binary variables (P and Q are thus boolean variables. Information about notation may be found in Bocheński (1959), Enderton (2001), and Quine (1982); for details about the operators, see the key below).
T = true and F = false. The Com row indicates whether an operator, op, is commutative – P op Q = Q op P. The L id row shown to the operator’s left identities if it has any values, I such that I op Q = Q. The R id row shown to the operator’s right identities if it has any values I such that P op I = P.[note 1]
The four combinations of input values for p, q, are read by row from the table above. The output function for each p, q combination, can be read, by row, from the table.
Key:
The key is oriented by column, rather than row. There are four columns rather than four rows, to display the four combinations of p, q, as input.
p: T T F F
q: T F T F