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In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. [ 1] This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasoning .
The deductive-nomological model ( DN model) of scientific explanation, also known as Hempel's model, the Hempel–Oppenheim model, the Popper–Hempel model, or the covering law model, is a formal view of scientifically answering questions asking, "Why...?". The DN model poses scientific explanation as a deductive structure, one where truth of ...
Transformation rules. In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms. [ 1][ 2]
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic . The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of ...
Deduction theorem. In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B, it is sufficient to assume A as a hypothesis and then proceed to derive B. Deduction theorems exist for both ...
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and " Socrates is a man" to the conclusion ...
Consistency. In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. [ 1] A theory is consistent if there is no formula such that both and its negation are elements of the set of consequences of . Let be a set of closed sentences (informally "axioms") and the set of closed sentences provable from ...
In logic and philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur[ 1] ( / ˌnɒn ˈsɛkwɪtər /; Latin for 'it does not follow') is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. [ 2]
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