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Constructive dilemma [1] [2] [3] is a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either P or R is true, then either Q or S has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too.
Another valid form of argument is known as constructive dilemma or sometimes just 'dilemma'. It does not leave the user with one statement alone at the end of the argument, instead, it gives an option of two different statements. The first premise gives an option of two different statements.
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible. The Curry–Howard correspondence between proofs and programs relates modus ponens to function application : if f is a function of type P → Q and x ...
A dilemma (from Ancient Greek δίλημμα (dílēmma) 'double proposition') is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. The possibilities are termed the horns of the dilemma, a clichéd usage, but distinguishing the dilemma from other kinds of predicament as a matter of usage.
Some troops leave the battlefield injured. Others return from war with mental wounds. Yet many of the 2 million Iraq and Afghanistan veterans suffer from a condition the Defense Department refuses to acknowledge: Moral injury.
His new friend has, for example, criticized the new British government of Labour Party Prime Minister Keir Starmer. And last week he endorsed Germany’s far-right party as the country struggles ...
Constructive / destructive dilemma; ... In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The ...