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Deductive reasoning. 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 ...
Logical reasoning is concerned with the correctness of arguments. A key distinction is between deductive and non-deductive arguments. Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion ...
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]
A deductive system is used to demonstrate, on a purely syntactic basis, that one formula is a logical consequence of another formula. There are many such systems for first-order logic, including Hilbert-style deductive systems, natural deduction, the sequent calculus, the tableaux method, and resolution. These share the common property that a ...
Syllogism. A syllogism ( 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. "Socrates" at the Louvre. In its earliest form (defined by Aristotle in his 350 BC book Prior ...
In propositional logic, modus ponens ( / ˈmoʊdəs ˈpoʊnɛnz /; 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.
In propositional logic, modus tollens ( / ˈmoʊdəs ˈtɒlɛnz /) ( 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. Not Q ...
The concept of proof is formalized in the field of mathematical logic. [ 12] A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones.