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
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