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Which card or cards must be turned over to test the idea that if a card shows an even number on one face, then its opposite face is blue? 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]
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 "mode that by denying denies") [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 ...
Mental logic theories hold that deductive reasoning is a language-like process that happens through the manipulation of representations using rules of inference. Mental model theories , on the other hand, claim that deductive reasoning involves models of possible states of the world without the medium of language or rules of inference.
In this way, it contrasts with deductive reasoning examined by formal logic. [35] Non-deductive arguments make their conclusion probable but do not ensure that it is true. An example is the inductive argument from the empirical observation that "all ravens I have seen so far are black" to the conclusion "all ravens are black".
A propositional argument using modus ponens is said to be deductive. In single-conclusion sequent calculi , modus ponens is the Cut rule. The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible .
Induction puzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction. [1] [2]A puzzle's scenario always involves multiple players with the same reasoning capability, who go through the same reasoning steps.
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.
For example, the proposition that water is H 2 O (if it is true): According to Kripke, this statement is both necessarily true, because water and H 2 O are the same thing, they are identical in every possible world, and truths of identity are logically necessary; and a posteriori, because it is known only through empirical investigation.