Satisfiabiliteits

Satisfiabiliteits, also known as satisfiability in English, is a fundamental concept in the field of mathematical logic and computer science, particularly within propositional and predicate logic. It refers to the question of whether a given logical formula or set of formulas can be satisfied by some assignment of truth values to its variables. In other words, a formula is satisfiable if there exists at least one interpretation or valuation that makes the formula true.

The concept of satisfiability is central to the domain of automated theorem proving, logic programming, and artificial intelligence. It underpins the operation of satisfiability solvers, commonly called SAT solvers, which are specialized algorithms designed to determine whether a propositional logic formula is satisfiable. These solvers are used in various applications, including hardware and software verification, planning, and cryptography.

A formula is considered unsatisfiable if no assignment of truth values can make it true. Conversely, a formula is satisfiable if such an interpretation exists. If a formula is both satisfiable and valid in all interpretations, it is said to be valid or logically valid, meaning it is true under every assignment.

The satisfiability problem (SAT problem) was the first problem proven to be NP-complete, highlighting its computational difficulty. Determining satisfiability is generally computationally intensive for large or complex formulas, but advances in algorithms and heuristics continue to improve the efficiency of SAT solving.

Overall, satisfiabiliteits is a key concept that drives research and development in logic, computational complexity, and practical problem-solving within computer science.