Relation (database) - Wikipedia
3 - The cardinality between two entities define the relationship. The cardinality of one data table known as: left table. inner table. of local table. with respect to. Every asymmetric relation is also an antisymmetric relation. Your proposal for Examples about reflexive and irreflexive (or anti-reflexive): the relation " is. Define a relation R that represents the relationship between people and classes. . Asymmetric relation . N-ary relations are the basis of relational database.
So the pairs, triples, etc. It is only ordered pairs, ordered triples, more generally, n-tuples or sequences that exhibit relations Kim There are a number of reasons we should be wary of characterising relations in such quasi-mathematical terms. We cannot avoid the difficulties associated with sequences by appealing to the Kuratowski definition of sequences in terms of unordered sets where, e.
There are indefinitely many other set-theoretic constructions upon which we may rely to model sequences, e. The next idea that needs to be introduced is the idea of a converse relation.
Before and after, above and below are prima facie examples of mutually converse relations. Non-symmetric relations, including asymmetric ones, are distinct from their converses if they have them. More generally, whilst a binary non-symmetric relation has only one converse, a ternary one has five mutual, distinct converses, a quadratic relation has 23 converses, etc. The issue of whether relations have converses is another issue to which we will return later. The final distinction we will need, or more accurately, family of distinctions, is between internal and external relations.
Different versions of the internal-external distinction correspond to different explanations of how internal relations are fixed Ewing The first version of the distinction is owed to Moore. If you essentially come from your biological parents then you could not have existed whilst failing to be their offspring, i.
The second version of the internal-external distinction is favoured by Armstrong b: The third version is owed to Lewis. Lewis intends his distinction to classify the same way. Glasgow is west of Edinburgh.
This tells us something about the locations of these two cities. But where is the relation that holds between them in virtue of which Glasgow is west of Edinburgh? Rather the relation must somehow share the divided locations of Glasgow and Edinburgh without itself being divided.
This may sound peculiar if we assume that middle-sized things like cities, which have locations in a relatively straightforward sense, set a standard for how entities in general ought to behave. Or even go down the route of conceiving relations as abstract, i.
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But is the price right? Do the theoretical benefits of admitting relations outweigh the cost of offending pre-theoretic intuition? But it only follows that relations are unsatisfactorily characterised if we assume that substances and attributes provide the benchmark for satisfactory characterisation.
If the price is right we should open our minds to the possibility of things which are neither fish nor fowl but vegetables, i. In the present section our focus will be upon whether to accept or reject external relations, before turning to internal relations in the next.
Bradley regarded himself the nemesis of external relations, but not only them. Famously, Bradley brought a vicious regress argument against external relations.
In his original version But positing more relations to fix up the problem is only throwing good money after bad. Bradley concluded that we should eliminate external relations from our ontology. Bradley assumed external relations to be general entities, i. But, it is argued, this problem can be avoided by either positing facts or tropes, which are particular rather than general entities.
Both of these purported solutions are open to question. It seems that they presuppose what they set out to show: Maurin and Simons argue that if we reject Bradley's assumption that relations are general entities, i. By way of analogy, consider the Problem of Evil: Of course if God exists then there cannot be any unnecessary evil, i. Reductionism about Internal Relations What about internal relations? Do we need to acknowledge their existence?
So, in one sense or another, it suffices for the obtaining of an internal relation that either the things it relates exist or that the things it relates have such-and-such intrinsic characters.
On this basis, some philosophers have concluded that there is no need to admit internal relations as additional pieces of furniture in the Universe Fisk Why do they think this? Nevertheless, all the truths about internal relations are determined by the existence or the intrinsic characters of the things they relate, or supervene upon them. Ben Vorlich, a Scottish mountain, is taller than Ben Vane, its neighbour. Ben Vorlich is ft high whilst Ben Vane is ft. This, broadly speaking, reductionist argument is open to question in a variety of respects.
Some philosophers have maintained that it cannot be effective because we literally perceive proportions and other internal relations Mulligan ; Hochberg To bring the issues here into focus we will need to take on board two further distinctions.
First, the distinction between truth-making and ontological commitment. Armed with the distinction between truth-making and ontological commitment, we are now able to state a very general shortcoming of the argument.
The second distinction we need is between thick and thin relations Mulligan Thin relations, by contrast to thick relations, are typically internal.
We are now equipped state another, more specific gap in the reductionist argument. The answer is that the thin relation being greater than holds between the number of feet in height that Ben Vorlich has and the number of feet in height that Ben Vane has Russell So internal relations may not in general be required to perform the role of truth-makers for comparative claims. Nonetheless thin internal relations may perform an indispensable role in explaining why the truth-makers for comparative claims are equipped to make such claims true, rather than leaving this a matter of brute inexplicable necessity—because, in this case, the heights of the mountains in question lie in a certain relation of proportion to one another.
This leaves us a choice. Or we can adopt the more austere view that only admits thin internal relations to hold amongst intrinsic characteristics Mulligan The situation may be summed up in schematic terms. The case against reductionism about internal relations has proceeded so far from a relatively a priori basis. It is often taken for granted by metaphysicians that the fundamental quantities of physics provide a ready source of monadic foundations because physical quantities are intrinsic characteristics.
But not only is this view contentious, there are many other notions in classical mechanics, such as force, stress, strain and elasticity, represented using vectors and tensors, that belie the conception of fundamental physical quantities as intrinsic Butterfield When we turn from classical mechanics to relativity theory and quantum theory, the a posteriori case against conceiving physical quantities as intrinsic is even stronger.
It also has momentum, stress and other traditionally mechanical properties. So mass is no longer conceived as an intrinsic property of localized lumps of stuff, let alone of point particles. Furthermore, the attribution of mass, momentum, stress, etc. So these quantities are not intrinsic, but, rather, relational properties. They are properties that the radiation or matter field in question has in virtue of its relation to spacetime structure Lehmkuhl In quantum theory there are even fewer candidates for intrinsic properties.
Turning to quantum field theory: There are not various quantum particles, each of them represented by a complex-valued field as above, and each of them, say, electrons. Rather there is a single all-pervading electron field and each electron, as treated in elementary quantum mechanics, is replaced by a unit of energetic excitation of the electron field.
The same goes for other types of matter, such as quarks. According to quantum field theory, quarks are really excitations of an all-pervading quark field. Besides, quantum field theory exhibits a second, and fundamentally different, way in which mass and charge fail to be intrinsic properties. So, to sum up this case against reductionism about relations: But this it is not the only case that has been made.
Consider next the related suggestion that spatio-temporal relations are internal relations between, variously, space-time points, regions or events Simons General relativity makes serious trouble for this suggestion.
The thinking behind the suggestion is that it belongs to the essential natures of space-time points, etc. From metrical essentialism it follows that the mere existence of a point, etc. Hence, it is argued, there is no need to admit spatio-temporal relations, or at least consider spatio-temporal relations as ontological additions to the furniture of the Universe.
asymmetrical | Definition of asymmetrical in English by Oxford Dictionaries
But, as well as the a priori concerns already aired, this argument for refusing to admit spatio-temporal relations as ontological additions is encumbered by the a posteriori difficulties of the metrical essentialism it presupposes.
These difficulties for metrical essentialism arise from the fact that in general relativity space-time structure varies from one model, i. We cannot leave points or regions to themselves to settle their internal relations, because general relativity denies the idea of a spatial-temporal framework whose make-up is settled independently of the matter or radiation. It may help to understand this debate about space-time points if we consider the following line of response on behalf of metrical essentialism.
According to metrical essentialism, points have their metrical properties and relations, i.
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So if the space-time framework differs between models then the points must differ between models too. What, however, this line of response fails to take into account is how extremely fragile spatio-temporal relations must be conceived to be when metrical essentialism is combined with general relativity. Take a possible world which is truly described by a dynamical theory of space-time i.
Now take a second possible world which differs from the first only with respect to a tiny change, on a millimeter scale as regards length, and on a milligram scale as regards mass. This involves altering spatio-temporal relations throughout the entire universe. If, instead of taking a duplicate of the electron and a duplicate of the proton, we take a duplicate of the whole atom, then it will exhibit the same electron-proton distance as the original atom.
Although distance fails to supervene on the intrinsic nature of the relata taken separately, it does supervene on the intrinsic nature of the composite of the relata taken together - in this case the composite hydrogen atom. Either 1 the composite is just the proton and electron taken together.
But then the distance between them fails to supervene upon the intrinsic character of the composite, because there are duplicates of the proton and duplicates of the electron that vary in distance. Or 2 the composite is more than just the proton and electron, i. Can this dilemma for Lewis be sidestepped by the following manoeuvre?
Suppose the composite is the mereological fusion of the proton and the electron. Then can't we say that the fusion has its intrinsic character, and the distance relation between the parts of the fusion supervenes on this character? But why believe such a theory? So the distance relation of the electron and fusion cannot supervene upon the intrinsic character of the proton-electron fusion. The Nature of Relations: Order and Direction Supposing they exist, what is the nature of relations, whether internal or external?
It is the crucial feature of binary non-symmetric relations, which distinguishes them from binary symmetric relations, or, more generally, distinguishes relations which fail to be strictly symmetric from strictly symmetric ones, that they bestow order upon the things they relate. Non-symmetric relations do so, because they admit of differential application, i.
But can we say anything more about how it is possible for non-symmetric relations to admit of differential application?
Such variables are classified into two classes: A base relation variable is a relation variable which is not derived from any other relation variables. In SQL the term base table equates approximately to base relation variable. A view can be defined by an expression using the operators of the relational algebra or the relational calculus.
Such an expression operates on one or more relations and when evaluated yields another relation. The result is sometimes referred to as a "derived" relation when the operands are relations assigned to database variables. A view is defined by giving a name to such an expression, such that the name can subsequently be used as a variable name.
Note that the expression must then mention at least one base relation variable. The following is an example. R is a relation on these n domains if it is a set of elements of the form d1, d2, One reason for abandoning positional concepts altogether in the relations of the relational model is that it is not at all unusual to find database relations, each of which has as many as 50,or even columns.
Communications of the ACM. Association for Computing Machinery.