Propositionsstrenge

Propositionsstrenge, or proposition strings, is a term used in formal logic and related fields to describe an ordered sequence of propositions that can function as premises in an argument or as components of a larger logical expression. The concept emphasizes the syntactic arrangement of individual propositions rather than a single, stand-alone statement.

In formal notation, a propositionsstrenge is typically represented as a finite sequence p1, p2, ..., pn. The meaning of the string depends on how the propositions are connected, if at all, by logical operators such as and, or, not, or implications. Without explicit connectives, the string is a mere list of propositions; with connectives, it yields a compound proposition or a structured argument.

A key distinction is that a propositionsstrenge itself is not automatically a proposition. To obtain a proposition, one must specify a semantic structure that combines the individual propositions with logical connectives. The truth-value of the resulting expression is then determined under a given valuation. In argumentation and proof theory, such strings are used to model sequences of premises and to analyze the validity of inferences or the application of inference rules.

Applications include teaching basic logic, formalizing syllogistic arguments, and programming language semantics where sequences of propositions represent states or assumptions. The notion also appears in discussions of argument structure, where a chain of premises leads to a conclusion.

See also: propositional logic, conjunction, implication, premises, inference, formal language.