In these notes, I will briefly discuss the topic “punctuating statements in propositional (or symbolic) logic.”
But why do we need to punctuate propositions in symbolic logic? This is because, in many instances, propositions in symbolic contain more than one connective; but in symbolic logic, all propositions should only have one major connective.
Thus, if there are two or more connectives, then we have to punctuate the proposition accordingly so that the major connective will become clear.
Symbolic logic uses parentheses ( ), brackets [ ], and braces { } as punctuation symbols.
Let us consider the example below.
If the road is wet, then either it rains today or the fire truck spills water on the road. (p, q, r)
As we can see, the example contains three propositions, namely:
1) The road is wet,
2) It rains today, and
3) The fire truck spills water on the road.
And as I already discussed in my previous posts, we learned that the variables provided after the proposition represent the propositions in the entire proposition respectively. Thus, in the example above, p stands for “The road is wet,” q for “It rains today,” and r for “The fire truck spills water on the road.” Hence, initially, the proposition is symbolized as follows:
p ⊃ q v r
However, the symbol above is not yet complete because, at this point, it is not yet clear what type of proposition it is. This is the reason why we need to punctuate the proposition. Please see my previous discussion on “Propositions and Symbols Used in Symbolic Logic” (see http://philonotes.com/index.php/2018/02/02/symbolic-logic/) for some idea on how to symbolize a proposition in symbolic logic.
Now, if we analyze the proposition, it would become clear that it is a conditional proposition whose consequent is an inclusive disjunction. For this reason, we need to punctuate the consequent.
Thus, the proposition “If the road is wet, then either it rains today or the fire truck spills water on the road” is symbolized as follows:
p ⊃ (q v r)
I will discuss more about this when I go to the discussion on “symbolizing propositions” in symbolic logic.
Meantime, let me give examples of a punctuated proposition just to show that statements in propositional or symbolic logic that contain two or more connectives have to be punctuated accordingly. Please see examples below then.
