Väitelausekkeita

Väitelausekkeita, known in English as propositional logic or sentential logic, is a fundamental branch of mathematical logic. It deals with propositions, which are declarative sentences that are either true or false. The core idea is to analyze the relationships between these propositions and how their truth values can be determined based on the truth values of simpler propositions.

In propositional logic, basic propositions are represented by symbols, typically letters like p, q, and r. These simple propositions can be combined using logical connectives to form more complex compound propositions. The most common connectives include: negation (not), conjunction (and), disjunction (or), implication (if...then...), and biconditional (if and only if).

The truth or falsity of a compound proposition is determined by the truth values of its constituent propositions and the specific connective used. This relationship is formally defined using truth tables. A truth table systematically lists all possible combinations of truth values for the basic propositions and shows the resulting truth value of the compound proposition for each combination.

Väitelausekkeita provides a formal system for reasoning about the logical structure of arguments. It allows us to determine whether an argument is valid, meaning that if the premises are true, the conclusion must also be true. This is achieved by analyzing the logical form of the argument rather than its specific content. Applications of propositional logic extend to computer science, artificial intelligence, philosophy, and mathematics.