sinngleich

Sinngleich is a German term used to describe expressions, statements, or formulas that share the same meaning or the same truth-conditions across interpretations. The word combines Sinn (sense or meaning) and gleich (equal) and is applied in logic, linguistics, and computer science to denote semantic equivalence rather than mere surface form.

In formal logic and mathematics, two propositions A and B are sinngleich if A and B are logically equivalent; that is, A ↔ B is a tautology (valid in all models). This notion is also called semantic equivalence. When two formulas are sinngleich, they yield the same truth-values under every possible interpretation.

Examples in logic include: p ∨ q and q ∨ p, which are sinngleich by the commutativity of disjunction; and p ∧ (p ∨ q) which is sinngleich to p (absorption). Conversely, p ∧ q is not sinngleich to p ∨ q, since they differ in truth conditions.

In linguistics and natural language, sinngleich refers to paraphrase: two sentences express the same proposition despite different wording. However, natural language is context-dependent and subject to ambiguity, so achieving perfect sinngleichness is often more complex than in formal systems.

In computer science and formal verification, semantic equivalence describes when two programs or expressions produce the same outputs for all valid inputs and states, possibly with identical side effects. This use of sinngleich underpins program optimization and correctness proofs.

Limitations include context-dependence, world knowledge, and presuppositions in natural language, which can prevent exact sinngleichness. The concept remains a central ideal in distinguishing meaning from mere form.