An interpretation of a truth-functional propositional calculus is an assignment to each propositional symbol of of one or the other (but not both) of the truth values truth (T) and falsity (F), and an assignment to the connective symbols of of their usual truth-functional meanings. An interpretation of a truth-functional propositional calculus may also be expressed in terms of truth tables.
For distinct propositional symbols there are distinct possible interpretations. For any particular symbol, for example, there are possible interpretations:
- is assigned T, or
- is assigned F.
For the pair, there are possible interpretations:
- both are assigned T,
- both are assigned F,
- is assigned T and is assigned F, or
- is assigned F and is assigned T.
Since has, that is, denumerably many propositional symbols, there are, and therefore uncountably many distinct possible interpretations of .
Read more about this topic: Propositional Calculus
Famous quotes containing the words interpretation of and/or calculus:
“It is clear that everybody interested in science must be interested in world 3 objects. A physical scientist, to start with, may be interested mainly in world 1 objects—say crystals and X-rays. But very soon he must realize how much depends on our interpretation of the facts, that is, on our theories, and so on world 3 objects. Similarly, a historian of science, or a philosopher interested in science must be largely a student of world 3 objects.”
—Karl Popper (1902–1994)
“I try to make a rough music, a dance of the mind, a calculus of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.”
—Judith Johnson Sherwin (b. 1936)