Concept
Soundness
Related concepts (17)
Formal system
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought.
Tautology (logic)
In mathematical logic, a tautology (from ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement.
Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises.
Premise
A premise or premiss is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. Arguments consist of a set of premises and a conclusion. An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are false, the argument says nothing about whether the conclusion is true or false. For instance, a false premise on its own does not justify rejecting an argument's conclusion; to assume otherwise is a logical fallacy called denying the antecedent.
Hilbert system
In mathematical physics, Hilbert system is an infrequently used term for a physical system described by a C*-algebra. In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal deduction attributed to Gottlob Frege and David Hilbert. These deductive systems are most often studied for first-order logic, but are of interest for other logics as well.
Semantics of logic
In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment. The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences.
Metalogic
Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths. The basic objects of metalogical study are formal languages, formal systems, and their interpretations.