Propositionaalinen

Propositionaalinen is a Finnish adjective used to describe things relating to propositions, especially in the context of propositional logic. Propositional logic is the formal system that studies the relationships between propositions and the truth-functional connectives that combine them.

In propositional logic, a proposition is a sentence that is either true or false. The logic operates with propositional variables (such as p, q, r) and connectives like not (¬), and (∧), or (∨), implies (→), and if and only if (↔). Formulas are built by applying these connectives to propositional variables. The semantics are truth-conditional: an interpretation assigns truth values to the variables, and the truth value of any formula is determined by truth tables.

Key concepts include tautologies (formulas that are true under every interpretation), satisfiability (there exists an interpretation that makes a formula true), and contradiction (false under every interpretation). Propositional logic also explores logical equivalence, implication, and the use of formal proof systems such as natural deduction or Hilbert-style systems, along with notions of soundness and completeness.

A common distinction is between propositionaalinen logiikka and predikaattilogiikka (predicate logic). The former focuses on the truth values of whole propositions and their connectives, while the latter extends to internal structure of statements with predicates and quantifiers.

Applications of propositionaalinen logic include analysis of arguments, design of digital circuits, formal verification, and foundational studies in computer science and artificial intelligence. It provides a compact, idealized framework for reasoning about truth-functional relationships.