Proposisjonale

Proposisjonale, in Norwegian, refers to the area of logic concerned with propositions and the formal systems that manipulate them. It describes both propositions themselves and formulas formed from them using logical connectives. In this context, a proposition is a statement that can be true or false, and proposisjonale logic studies how these truth values combine under logical operations.

Proposisjonale formulas are built from a set of proposisjonale variables, usually denoted by p, q, r, and so on, together with connectives such as conjunction (and), disjunction (or), negation (not), implication (if ... then), and biconditional (if and only if). Parentheses are used to specify the structure of expressions. Common examples include p ∧ q, p ∨ q, ¬p, p → q, and p ↔ q.

Semantics in proposisjonale logic relies on valuations: mappings from each proposisjonale variable to a truth value, true or false. The truth value of any complex formula is determined by truth tables for the connectives. For instance, p ∧ q is true exactly when both p and q are true; p → q is false only when p is true and q is false; p ↔ q is true when p and q share the same truth value.

This form of logic is the simplest foundational system in mathematical logic. It excludes quantifiers and relations among objects, focusing instead on the logical relationships between propositions. Applications include digital circuit design, formal verification, and reasoning tasks where statements can be abstracted to truth-functional variables. The core problems—tautology testing, satisfiability, and logical consequence—are well-studied, with satisfiability known to be NP-complete. Proposisjonale logic provides a stepping stone to more expressive systems, such as predicate and modal logics.