Search results
Results From The WOW.Com Content Network
Strong soundness of a deductive system is the property that any sentence P of the language upon which the deductive system is based that is derivable from a set Γ of sentences of that language is also a logical consequence of that set, in the sense that any model that makes all members of Γ true will also make P true.
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.
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 ...
Sanity (from Latin: sānitās) refers to the soundness, rationality, and health of the human mind, as opposed to insanity.A person is sane if they are rational.In modern society, the term has become exclusively synonymous with compos mentis (Latin: compos, having mastery of, and Latin: mentis, mind), in contrast with non compos mentis, or insanity, meaning troubled conscience.
Soundness guarantees that all possible behaviours are preserved while completeness guarantees that no behaviour is added by the encoding. In particular, in the case of compilation of a programming language, soundness and completeness together mean that the compiled program behaves accordingly to the high-level semantics of the programming language.
In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors.Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a ...
Unlike natural languages, such as English, the language of first-order logic is completely formal, so that it can be mechanically determined whether a given expression is well formed. There are two key types of well-formed expressions: terms , which intuitively represent objects, and formulas , which intuitively express statements that can be ...
Leon Henkin (1950) defined an alternative kind of semantics for second-order and higher-order theories, in which the meaning of the higher-order domains is partly determined by an explicit axiomatisation, drawing on type theory, of the properties of the sets or functions ranged over. Henkin semantics is a kind of many-sorted first-order ...