DERIVABILITY Meaning and
Definition
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Derivability is a term used in logic and mathematics to describe the property of a statement or formula being able to be derived or deduced from a set of given premises or axioms. It refers to the possibility of showing the logical connection or inference between different statements or propositions using the rules of logical reasoning.
In formal logic, derivability is often associated with systems of formal proofs or deduction systems. It involves the process of constructing a valid argument or proof step-by-step, starting from a set of initial assumptions or axioms, and using specific rules of inference to establish the truth of a given statement or formula. The concept of derivability is fundamental in determining the validity or soundness of logical arguments, as it allows for the systematic demonstration of the logical entailment or consequence relation between different statements.
In mathematics, derivability is closely related to the notion of mathematical proofs. It signifies the ability to demonstrate the truth or falsity of a mathematical proposition or theorem based on a set of previously established mathematical truths. The process of derivability in mathematics often involves the use of various mathematical techniques, such as logical deductions, mathematical induction, or the application of mathematical theorems and properties.
Overall, derivability refers to the capacity to derive or deduce new statements or formulas from given premises or axioms, and it plays a crucial role in formal logic and mathematics in establishing the validity and coherence of logical and mathematical arguments.
Common Misspellings for DERIVABILITY
- serivability
- xerivability
- cerivability
- ferivability
- rerivability
- eerivability
- dwrivability
- dsrivability
- ddrivability
- drrivability
- d4rivability
- d3rivability
- deeivability
- dedivability
- defivability
- detivability
- de5ivability
- de4ivability
- deruvability
- derjvability
Etymology of DERIVABILITY
The word "derivability" is formed from the root word "derive", which originates from the Old French word "deriver" meaning "to derive or lead from a source". The suffix "-ability" is added to form a noun meaning "the state or quality of being capable or able to derive or be derived". Therefore, "derivability" is derived from the concept of being able to derive or have something derived from a source.
