Propositional logic · Definition
Proposition
A proposition is the basic object of propositional logic: a statement that can be true or false, but not both.
Definition
A proposition is a declarative statement that is assigned one of the truth values \(\top\) or \(\bot\).
A proposition is the basic unit of propositional logic: a declarative statement that can be assigned exactly one of two truth values, true or false.
Propositional logic does not investigate by itself whether a statement correctly describes the world. It takes propositions and their values as a starting point to study how they combine and what consequences follow from them.
That is why a question, a command or an open expression such as x > 2 does not work as a complete proposition without additional information.
Think about it
Why is "is it raining?" not a proposition by itself?
Because it is a question and does not assert something to which we can directly assign true or false.
Exercises 10
- A logical proposition can have as truth value...
- Propositional logic takes as its basic unit...
- Which statement best describes a proposition?
- What does propositional logic not decide by itself?
- Let \(P\) be a proposition. Which of the following statements about \(P\) is impossible?
- Which statement is a proposition?
- The truth value of a classical proposition is...
- Which of these expressions is not a proposition by itself?
- A proposition cannot simultaneously have...
- What does the letter \(P\) represent in propositional logic?
What comes next
References
- Frederic P. Schuller, Lectures on the Geometrical Anatomy of Theoretical Physics · Lecture 1, Introduction / Logic of Propositions and Predicates, YouTube, 2015.