Significantly, modal logics can be developed to accommodate most of these idioms ; it is the fact of their common logical structure ( the use of " intensional " sentential operators ) that make them all varieties of the same thing.

This is of course not an obvious thing to assume, but if we interpret as provability in Peano Arithmetic, then the existence of modal fixed points is in fact true.

DeRose adopts a type of modal or " safety " ( as it has since come to be known ) account on which knowledge is a matter of one's belief as to whether or not p is the case matching the fact of the matter, not only in the actual world, but also in the sufficiently close possible worlds: Knowledge amounts to there being no " nearby " worlds in which one goes wrong with respect to p. But how close is sufficiently close?

It's here that DeRose takes the modal account of knowledge in a contextualist direction, for the range of " epistemically relevant worlds " is what varies with context: In high standards contexts one's belief must match the fact of the matter through a much wider range of worlds than is relevant to low standards contexts.

He himself advances a more " moderate " realism about possible worlds, which he terms modal actualism ( since it holds that all that exists is in fact actual, and that there are no " merely possible " entities.

As the user stories pass their acceptance criteria, the business owners can be sure of the fact that the developers are progressing in the right direction about how the application was envisaged to work and so it's essential that these tests include both business logic tests as well as UI validation elements ( if need be ).

The problem with the psychological approach to mathematics and logic is that it fails to account for the fact that this approach is about formal categories, and not simply about abstractions from sensibility alone.

However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he proves is in fact intuitionistically true.

With the omission of the law of the excluded middle as an axiom, the remaining logical system has an existence property which classical logic does not: whenever is proven constructively, then in fact is proven constructively for ( at least ) one particular, often called a witness.

Despite its advantages, the concept of implementing the game logic in a separate scripting language and writing an interpreter for it was soon dropped ( even by John Carmack who had implemented this concept ) because of the overall inflexibility of an interpreted language, the increasingly complex game logic and the fact that the game logic could be packaged into a native Dynamic link library whose source code could be released to the mod community.

The deviation from the relational model arises from the fact that the implementation of this ad hoc concept in SQL involves the use of three-valued logic, under which the comparison of NULL with itself does not yield true but instead yields the third truth value, unknown ; similarly the comparison NULL with something other than itself does not yield false but instead yields unknown.

" This debate obscured the fact that semantics networks, at least those with well-defined semantics, are a form of logic.

Or rather, to admit frankly the fact of non-identity and to follow through its logic to the end.

This GPU is unique in the fact that almost all of its 1. 4 billion transistors are used for logic, in contrast to the Itanium, whose large transistor count is largely due to its 24 MB L3 cache.

As a matter of fact, it is becoming very difficult to find 10BASE2-compatible network cards as distinct pieces of equipment, and integrated LAN controllers on motherboards don't have the connector, although the underlying logic may still be present.

In fact, the Spartans were also rigorously trained in logic and philosophy.

This applies not only to matters of fact, but also to " relations of ideas ," as Hume called them: the structures of logic which interpret, organize and abstract observations.

The axiom M by itself is not canonical ( Goldblatt, 1991 ), but the combined logic S4. 1 ( in fact, even K4. 1 ) is canonical.

The term itself inspires a certain skepticism, sounding equivalent to " half-baked logic " or " bogus logic ", but the " fuzzy " part does not refer to a lack of rigour in the method, rather to the fact that the logic involved can deal with concepts that cannot be expressed as " true " or " false " but rather as " partially true ".

The words " complementary-symmetry " refer to the fact that the typical digital design style with CMOS uses complementary and symmetrical pairs of p-type and n-type metal oxide semiconductor field effect transistors ( MOSFETs ) for logic functions.

The basic form is a series of questions formulated as tests of logic and fact intended to help a person or group discover their beliefs about some topic, exploring the definitions or logoi ( singular logos ), seeking to characterize the general characteristics shared by various particular instances.

* Where the teacher makes an error of logic or fact, it is acceptable for a student to draw attention to the error.

This fact is sometimes thought to have severe consequences for the program of logicism proposed by Gottlob Frege and Bertrand Russell, which aimed to define the natural numbers in terms of logic ( Hellman 1981, p. 451 – 468 ).

The use of these types of diagrams in formal logic, according to Ruskey and M. Weston, is " not an easy history to trace, but it is certain that the diagrams that are popularly associated with Venn, in fact, originated much earlier.

Accordingly, this line of logic concludes, we cannot in fact be sure beyond doubt about the nature of reality.

If we are going to appeal to force, if force is to be the arbiter to which we appeal, it would at least make common sense to try to make sure beforehand that we have got it, even if you accept that abysmal logic, that decadent point of view. We are in fact in the position today of having appealed to force in the case of a small nation, where if it is appealed to against us it will result in the destruction of Great Britain, not only as a nation, but as an island containing living men and women.

In fact, one important aspect of their very religion is the annihilation of men ''.

In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.

The fact is due mainly to international wars, both hot and cold.

While the pattern is uneven, some having gained more than others, nationalism has in fact served the Western peoples well.

In point of fact, this is a beige box with a bright red door, about one and a half feet square and hung from the wall about six feet from the door to Wisman's right.

The fact is that the Southern Confederacy differed from the earlier one almost as much as the Federal Constitution did.

To my knowledge, Lincoln remains the only Head of State and Commander-in-Chief who, while fighting a fearful war whose issue was in doubt, proved man enough to say this publicly -- to give his foe the benefit of the fact that in all human truth there is some error, and in all our error, some truth.

In fact the accumulation of the hardware of destruction is day by day increasing our fear of each other.

The new fact the initiates of this cult have to learn is that they must move toward simplicity.

The magic circle is, in fact, a symbol of and preparation for the metaphysical orgasm ''.

Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.

`` I may possibly be a greater risk than is the normal person of my age '', the President had said on February 29th of the election year, ignoring the fact that no one of his age had ever lived out another term.

In the incessant struggle with recalcitrant political fact he learns to focus the essence of a problem in the significant detail, and to articulate the distinctions which clarify the detail as significant, with what is sometimes astounding rapidity.

we accord it its place there, and in Lawrence's treatment we are given the innocent fantasy of a child, in fact, the form in which oedipal love is expressed in childhood.

There is probably some significance in the fact that two of the best incest stories I have encountered in recent years are burlesques of the incest myth.

How much they esteemed him is shown by the fact that their underground committee selected him as one of the few who would be helped to escape.

That is not to deny that he has been aware of traditions, of course, that he is steeped in them, in fact, or that he has dealt with them, in his books.

There is evidence to suggest, in fact, that many authors of the humorous sketches were prompted to write them -- or to make them as indelicate as they are -- by way of protesting against the artificial refinements which had come to dominate the polite letters of the South.

It seems quite obvious that all the really difficult tasks of human beings arise from the fact that man is not one, but many.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

Perhaps the mere fact that by plucking on the nerves nature can awaken in the most ordinary of us, temporarily anyway, the sleeping poet, and in poets can discover their immortality, is the most remarkable of all the remarkable phenomena to which we can attest??