Knowra Formal science Formal science Formal science studies abstract structures and rule-governed systems through deduction, proof, and symbolic representation. Its disciplines include mathematics, logic, and theoretical computer science.
Formal system : A set of symbols and rules that defines well-formed expressions and their derivations. Formal sciences investigate structures built from explicit symbols and rules.
Mathematics : The study of quantity, structure, space, and change through abstract reasoning. Mathematics is the oldest and broadest discipline commonly classified as formal science.
Mathematical proof : A deductive argument that establishes a mathematical statement from definitions, axioms, and prior results. It exemplifies how formal science justifies claims without experimental measurement.
Euclid's Elements : An ancient Greek mathematical treatise that organized geometry and number theory through definitions, axioms, and proofs. Its axiomatic presentation became a durable model of mathematical exposition.
Entscheidungsproblem : The question of whether an algorithm can decide the validity of every statement in first-order logic. Its negative resolution exposed a boundary on mechanical proof checking.
Axiom : A statement accepted as a starting assumption within a formal theory. Axioms provide premises from which formal theories derive further statements.
Mathematical logic : The mathematical study of formal languages, proof, and logical consequence. It applies mathematical methods directly to reasoning and formal systems.
Model theory : The study of the relationships between formal languages and the structures that satisfy them. It connects symbolic theories to the mathematical structures in which they hold.
Leibniz's characteristica universalis : Gottfried Wilhelm Leibniz's proposed universal symbolic language for representing concepts and resolving disputes by calculation. It anticipated the ambition to make reasoning precise through symbolic systems.
Turing machine : An abstract machine that formalizes step-by-step computation using a tape, symbols, and transition rules. It supplied a precise model for defining and analyzing computation.
Show all 28