Implicit Use of Biconditionals
The last article, part one of this topic, ended with a discussion of bi-conditionals, what it is, and their truth table. In Natural Language bi-conditionals are not always explicit. In particular, the if construction (if and only if) is rarely used in the common language. Instead, bi-conditionals are often expressed using “if, then” or an “only if” construction. The other part of the “if and only if” is implicit, i.e. the converse is implied but not stated. For example consider the following statement, “If you complete your homework, then you can go out and play”. What is really meant is “You can go out and play if and only if you complete your homework”. This statement is logically equivalent to two statements, “If you complete your homework, then you can go out and play” and “You can go out and play only if you complete your homework”. Because of this imprecision in Natural Language, an assumption needs to be made whether a conditional statement in natural language includes its converse or not.
Propositional Logic – Set 2
This article explores fundamental laws and concepts in the algebra of propositions like Idempotent, Associative, Distributive, and Commutative Laws, as well as special conditional statements.