Statement scheme

The term statement scheme (also: Statements scheme; plural: statement schemes) is partly as a synonym for the expression form of expression used, but specifically a concept of propositional logic and is an expression of propositional variables , or variables for propositional formulas contains and which merges into a statement, if you replace these variables with arbitrary statements.

The statement schema must be strictly distinguished from the statement variables occurring in it.

In propositional logic , a statement scheme has the same syntactic structure as a logical statement :

One differentiates by induction on the structure

• atomic formulas (atomic statement schemes): These are statement variables (x, y, ...) whose truth value may not be known.
• Compound formulas (compound statement schemes): If formulas are, so too . ${\displaystyle p,q}$ ${\displaystyle \neg p,\,p\vee q,\,p\wedge q,\,p\rightarrow q,\,p\leftrightarrow q}$

1. Sometimes the truth values (true) and (false) are also allowed with the atomic statement schemes . ${\displaystyle \top }$ ${\displaystyle \bot }$
2. Sometimes you can find in the literature that in the definition of the syntax only a subset of the formation of the statement scheme connectives is approved, including in any case . The remaining junctions are then usually derived from these and taken as an abbreviation. ${\displaystyle (\neg ,\vee ,\wedge ,\rightarrow ,\leftrightarrow )}$ ${\displaystyle \neg }$
3. The assignment of all free variables turns the statement into a logical statement.

literature

• Rainbow / Meyer, Dictionary of Philosophical Terms (2005) / Statement scheme
• Spies, Introduction to Logic (2004), p. 15
• Detel, Basic Course Philosophy I: Logic (2007), p. 70

Individual evidence

1. ↑ Lorenzen, Formal Logic, 4th ed. (1970), p. 32 f.