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In logic and deductive reasoning, an argument is sound if it is both valid in form and has no false premises. [1] Soundness has a related meaning in mathematical logic, wherein a formal system of logic is sound if and only if every well-formed formula that can be proven in the system is logically valid with respect to the logical semantics of the system.
Semantic completeness is the converse of soundness for formal systems. A formal system is complete with respect to tautologousness or "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system ...
Sound is defined as "(a) Oscillation in pressure, stress, particle displacement, particle velocity, etc., propagated in a medium with internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillation.
Argument terminology used in logic. In logic, an argument is a set of related statements expressing the premises (which may consists of non-empirical evidence, empirical evidence or may contain some axiomatic truths) and a necessary conclusion based on the relationship of the premises.
The word "logic" originates from the Greek word logos, which has a variety of translations, such as reason, discourse, or language. [4] Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments.
A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system. If some specific deductive system of first-order logic is sound and complete, then it is "perfect" (a formula is provable if and only if it is logically valid), thus equivalent to any other deductive system with the same ...
The correspondence between the sequent calculus and natural deduction is a pair of soundness and completeness theorems, which are both provable by means of an inductive argument. Soundness of ⇒ wrt. ⊢ If Γ ⇒ A, then Γ ⊢ A. Completeness of ⇒ wrt. ⊢ If Γ ⊢ A, then Γ ⇒ A.
A sailor and a man on shore, both sounding the depth with a line. Depth sounding, often simply called sounding, is measuring the depth of a body of water.Data taken from soundings are used in bathymetry to make maps of the floor of a body of water, such as the seabed topography.