The inference is overwhelming that Du Pont's commanding position was promoted by its stock interest and was not gained solely on competitive merit ''.

Men, trees, automobiles, houses, and so on -- objects continually confronted in everyday life -- had each its characteristic blot-appearance and became easily recognizable, at the very beginning of tracing, by an inference as to what each was.

The scholar William Mitford suggested that Pelopidas was taken prisoner in battle, but the language of Demosthenes hardly supports such an inference.

Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called " inverse probability " ( because it infers backwards from observations to parameters, or from effects to causes ).

A decision-theoretic justification of the use of Bayesian inference ( and hence of Bayesian probabilities ) was given by Abraham Wald, who proved that every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.

A possible inference is, that one can not be blamed for mistaken judgements if the motivation was to do good.

A theory of statistical inference was developed by Charles S. Peirce in " Illustrations of the Logic of Science " ( 1877 – 1878 ) and " A Theory of Probable Inference " ( 1883 ), two publications that emphasized the importance of randomization-based inference in statistics.

This type of refutation is valid only if the inference was from one Scripture, not if it was from two Scriptures.

This adds support to the inference that, at least at the beginning of his reign, Jehu was supported by the pro-Jehovah faction.

You might make some inference about the probability of heads and whether the coin was fair.

Popper thought that falsifiability was a better criterion because it did not invite the philosophical problems inherent in verifying an inductive inference, and it allowed statements from the physical sciences which seemed scientific but which did not satisfy the verification criterion.

Therefore, when a merger with a controlling stockholder was: 1 ) negotiated and approved by a special committee of independent directors ; and 2 ) conditioned on an affirmative vote of a majority of the minority stockholders, the business judgment standard of review should presumptively apply, and any plaintiff ought to have to plead particularized facts that, if true, support an inference that, despite the facially fair process, the merger was tainted because of fiduciary wrongdoing .″

The popularly held beliefs that Satan was once a prideful angel who eventually rebels against God, however, are not portrayed explicitly in the Bible and are mostly based on inference ( e. g., Ezekiel 28 and Isaiah 14: 12 – 17 ).

This inference is based on the fact that the term was used in two different ways during the republican era: during Terence's lifetime, it was used to refer to non-Carthaginian Libyco-Berbers, with the term Punicus reserved for the Carthaginians.

The evidence was seen as supporting the inference from the " Fighting Dinosaurs " fossil that Protoceratops was part of the diet of Velociraptor.

Upon further trial with heat, he was further convinced of the correctness of this inference, by finding that the India rubber could not be melted in boiling sulfur at any heat, but always charred.

By inference Tacitus was criticizing his own Roman culture for getting away from its roots — which was the perennial function of such comparisons.

The inference was obtained by cooling an exciton state below 5 K and further observing coherent light emission ( with interference patterns ) from it.

The second level is a sort of implicit inference that usually follows immediately the episode of knowing p ( knowledge simpliciter ).

Solomonoff's inductive inference is a mathematical proof of a statement akin to Occam's razor, under the assumption that the environment follows some unknown but computable probability of distribution.

Applying a conception of such illocutionary acts according to which they are ( roughly ) acts of saying something with the intention of communicating with an audience, he describes indirect speech acts as follows: " In indirect speech acts the speaker communicates to the hearer more than he actually says by way of relying on their mutually shared background information, both linguistic and nonlinguistic, together with the general powers of rationality and inference on the part of the hearer.

People readily make the modus ponens inference, that is, given if A then B, and given A, they conclude B, but only about half of participants in experiments make the modus tollens inference, that is, given if A then B, and given not-B, only about half of participants conclude not-A, the remainder say that nothing follows ( Evans et al., 1993 ).

* Formal proof or derivation, a sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference

When a valid argument is used to derive a false conclusion from false premises, the inference is valid because it follows the form of a correct inference.

* The syllogism is an inference in which one proposition ( the " conclusion ") follows of necessity from two others ( the " premises ").

A formal proof or derivation is a finite sequence of propositions ( called well-formed formulas in the case of a formal language ) each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference.

Intuitively, the algorithm follows all chains of inference after making each of its choices ; this either leads to a contradiction and a backtracking step, or, if no contradiction is derived, it follows that the choice was a correct one that leads to a satisfying assignment.

# From rule of inference 1, it follows that.

# From 4 and rule of inference 3, it follows that.

# From rule of inference 3, it follows that

# From rule of inference 2, it follows that

# From 11 and rule of inference 1, it follows that

A categorial grammar consists of two parts, a lexicon, which assigns a set of types ( also called categories ) to each basic symbol, and some type inference rules, which determine how the type of a string of symbols follows from the types of the constituent symbols.

A formal proof or derivation is a finite sequence of sentences ( called well-formed formulas in the case of a formal language ) each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference.

If found, res ipsa loquitur creates an inference of negligence, although in most cases it does not necessarily result in a directed verdict.

If evidence is simultaneously used to update belief over a set of exclusive and exhaustive propositions, Bayesian inference may be thought of as acting on this belief distribution as a whole.

If A ∧ B is true, then B ∧ A is true ; This derivation can be drawn by composing inference rules in such a fashion that premises of a lower inference match the conclusion of the next higher inference.

If G were provable under the axioms and rules of inference of T, then T would have a theorem, G, which effectively contradicts itself, and thus the theory T would be inconsistent.

Bertrand Russell discussed the paradox briefly in § 38 of The Principles of Mathematics ( 1903 ), distinguishing between implication ( associated with the form " if p, then q "), which he held to be a relation between unasserted propositions, and inference ( associated with the form " p, therefore q "), which he held to be a relation between asserted propositions ; having made this distinction, Russell could deny that the Tortoise's attempt to treat inferring Z from A and B is equivalent to, or dependent on, agreeing to the hypothetical " If A and B are true, then Z is true.

If f is the Gödel mapping and if formula C can be derived from formulas A and B through an inference rule r ; i. e.

If a chi squared test is conducted on a sample with a smaller size, then the chi squared test will yield an inaccurate inference.

For example, the rule of inference modus ponens takes two premises, one in the form of " If p then q " and another in the form of " p " and returns the conclusion " q ".

Given a counterfactual conditional, e. g., ' If there had been a circle on the blackboard then there would have been a triangle ', and the subsequent information ' in fact there was no triangle ', participants make the modus tollens inference ' there was no circle ' more often than they do from an indicative conditional ( Byrne and Tasso, 1999 ).

An inference engine using forward chaining searches the inference rules until it finds one where the antecedent ( If clause ) is known to be true.

If the structures that encode memory and personality are sufficiently intact that inference of the memory and personality are feasible in principle, and therefore restoration to an appropriate functional state is likewise feasible in principle, then the person is not dead.

If the previous data is not present, it is required for new inference.

If exact inference is computationally prohibitive, one may at

If these were the only data available, maximum parsimony would tend to group crocodiles with humans, and birds with bats ( as would any other method of phylogenetic inference ).

If a Bayesian network has the structure of a polytree, then belief propagation may be used to perform inference efficiently on it.

If the most general unifier is used in condensed detachment, then the logical result is the most general conclusion that can be made in the given inference with the given second expression.