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Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science.Informally, a quantified statement "such that …" can be viewed as a question "When is there an such that …?", and the statement without quantifiers can be viewed as the answer to that question.
The rational consequence relation is non-monotonic, and the relation is intended to carry the meaning theta usually implies phi or phi usually follows from theta.In this sense it is more useful for modeling some everyday situations than a monotone consequence relation because the latter relation models facts in a more strict boolean fashion—something either follows under all circumstances or ...
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
For example, in every logical system capable of expressing the Peano axioms, the Gödel sentence holds for the natural numbers but cannot be proved. Here a logical system is said to be effectively given if it is possible to decide, given any formula in the language of the system, whether the formula is an axiom, and one which can express the ...
Sometimes used for “relation”, also used for denoting various ad hoc relations (for example, for denoting “witnessing” in the context of Rosser's trick). The fish hook is also used as strict implication by C.I.Lewis p {\displaystyle p} ⥽ q ≡ ( p → q ) {\displaystyle q\equiv \Box (p\rightarrow q)} .
Monty Hall problem, also known as the Monty Hall paradox: [2] An unintuitive consequence of conditional probability. Necktie paradox: A wager between two people seems to favour them both. Very similar in essence to the Two-envelope paradox. Proebsting's paradox: The Kelly criterion is an often optimal strategy for maximizing profit in the long ...
Example 4 If the U.S. Congress passes a bill, the president's signing of the bill is sufficient to make it law. Note that the case whereby the president did not sign the bill, e.g. through exercising a presidential veto, does not mean that the bill has not become a law (for example, it could still have become a law through a congressional ...
This general strategy is a component of the general social contract view in political philosophy (for examples, see Gauthier (1986) and Kavka (1986)). [ d ] Other authors have attempted to use evolutionary game theory in order to explain the emergence of human attitudes about morality and corresponding animal behaviors.
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