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In a Hilbert system, the premises and conclusion of the inference rules are simply formulae of some language, usually employing metavariables.For graphical compactness of the presentation and to emphasize the distinction between axioms and rules of inference, this section uses the sequent notation instead of a vertical presentation of rules.
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as "P implies Q. P is true. Therefore, Q must ...
The ability of deductive reasoning is an important aspect of intelligence and many tests of intelligence include problems that call for deductive inferences. [1] Because of this relation to intelligence, deduction is highly relevant to psychology and the cognitive sciences. [ 5 ]
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Deductive reasoning is a basic form of valid reasoning, commencing with a general statement or hypothesis, then examines the possibilities to reach a specific, logical conclusion’. [10] This scientific method utilises deductions, to test hypotheses and theories, to predict if possible observations were correct.
Non-deductive reasoning is an important form of logical reasoning besides deductive reasoning. It happens in the form of inferences drawn from premises to reach and support a conclusion, just like its deductive counterpart. The hallmark of non-deductive reasoning is that this support is fallible.
In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "method of removing by taking away") [2] and denying the consequent, [3] is a deductive argument form and a rule of inference. Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q ...
For the most part this discussion of logic deals only with deductive logic. Abductive reasoning is a form of inference which goes from an observation to a theory which accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not ...