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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 ]
The Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966. [1] [2] [3] It is one of the most famous tasks in the study of deductive reasoning. [4] An example of the puzzle is: You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other.
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.
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal ...
Download as PDF; Printable version; ... Deduction and induction may refer to: Deductive reasoning; Inductive reasoning; Validity (logic)
In a Hilbert system, a formal deduction (or proof) is a finite sequence of formulas in which each formula is either an axiom or is obtained from previous formulas by a rule of inference. These formal deductions are meant to mirror natural-language proofs, although they are far more detailed.
In practice, it is usually enough to know that we could do this. We normally use the natural-deductive form in place of the much longer axiomatic proof. First, we write a proof using a natural-deduction like method: Q 1. hypothesis Q→R 2. hypothesis; R 3. modus ponens 1,2 (Q→R)→R 4. deduction from 2 to 3; Q→((Q→R)→R) 5. deduction ...
The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus (of some formal system) to the previous well-formed formulas in the proof sequence.