Is there a way in GraphDB 10.0.0 to safe the conclusions of different rules in different named graphs or contexts?
For example, if I have two rules like this:
id: rule1
x a <:Article>
y a <:Author>
--------------------
y <:mightWrite> x [Context: base_context:c1]
id: rule2
x a <:Book>
y a <:Author>
--------------------
y <:mightWrite> x [Context: base_context:c2]
Reasoning would lead to the results of both rules being stored within context onto:implicit instead of, what I would have expected, base_context:c1 and base_context:c2. Thus, is there a way to do such splitting of the readoning results?
Thank you in advance!
Related
I am totally new in answer set proramming (ASP Core-2 with Clingo) and am struggling with a problem I have not been able to solve.
The goal is to solve the 'Hamiltonian Path' problem, which is described as follows:
In a directed graph we're looking for a path which visits all nodes of the graph exactly once.
We can assume that all edge relations are known as facts, and that the input graph does actually contain a Hamiltonian Path. The desired output are the predicates
visited(NodeName, StepInOrder)
that each contains a node and the number at which step this node is reached. So for example, an output could be
visited(a, 1), visited(c, 2), visited(b, 3)
See my code below. The problem is, that at the last line, the program seems to enter an infinite loop. And I do not understand what the cause of this could probably be.
% pick one random start node
1 <= {startNode(N) : node(N)} <= 1.
% define helper predicate inPath which is true once and false once for each edge of the graph
{inPath(X, Y)} :- edge(X,Y).
% create possible paths
visited(X, 1) :- startNode(X).
visited(Y, C+1) :- visited(X, C), inPath(X, Y), not visited(Y, _). % infinite loop here
% some killing constraints to eliminate invalid solution candidates...
My guess is, that the program is generating an infinite number of answer sets, which all differ in their #stepInOrder value, because of some sort of cycle, but I thought this should be prevented by the not visited(Y, _).
If you need any additional context, let me know. Thanks in advance!
Lets go through your code:
1 <= {startNode(N) : node(N)} <= 1.
I guess this works, but just writing 1 {startNode(N) : node(N)} 1. or {startNode(N) : node(N)} == 1. would do the same.
% define helper predicate inPath which is true once and false once for each edge of the graph
{inPath(X, Y)} :- edge(X,Y).
This one works, allthough there are more efficient approaches to write it.
% create possible paths
visited(X, 1) :- startNode(X).
visited(Y, C+1) :- visited(X, C), inPath(X, Y), not visited(Y, _). % infinite loop here
You basically say: a node Y is visited at time C+1, if a node X was visited at time C, there is a path from X to Y, and at no time Y was visited or will be visited. So you clearly want to generate something but if you generate it you violate the rule which generated it. In clingo atoms can not change values. If an atom is labeled as True, it is True the whole time.
So I would probably write something like this:
1 { visited(Y,C+1) : inPath(X,Y) } 1 :- visited(X, C).
which reads: given X is visited at time C, the number of outgoing marked edges from X to any node Y is exactly 1. Mark Y as visited at time C+1.
All what is missing now, is a constraint to include all nodes to be visited.
You might want to have a look at this question from around the same time. The solution of the user has a different approach, he or she does not assign numbers to the nodes to indicate an order.
For an experiment I need to pseudo randomize a vector of 100 trials of stimulus categories, 80% of which are category A, 10% B, and 10% C. The B trials have at least two non-B trials between each other, and the C trials must come after two A trials and have two A trials following them.
At first I tried building a script that randomized a vector and sort of "popped" out the trials that were not where they should be, and put them in a space in the vector where there was a long series of A trials. I'm worried though that this is overcomplicated and will create an endless series of unforeseen errors that will need to be debugged, as well as it not being random enough.
After that I tried building a script which simply shuffles the vector until it reaches the criteria, which seems to require less code. However now that I have spent several hours on it, I am wondering if these criteria aren't too strict for this to make sense, meaning that it would take forever for the vector to shuffle before it actually met the criteria.
What do you think is the simplest way to handle this problem? Additionally, which would be the best shuffle function to use, since Shuffle in psychtoolbox seems to not be working correctly?
The scope of this question moves much beyond language-specific constructs, and involves a good understanding of probability and permutation/combinations.
An approach to solving this question is:
Create blocks of vectors, such that each block is independent to be placed anywhere.
Randomly allocate these blocks to get a final random vector satisfying all constraints.
Part 0: Category A
Since category A has no constraints imposed on it, we will go to the next category.
Part 1: Make category C independent
The only constraint on category C is that it must have two A's before and after. Hence, we first create random groups of 5 vectors, of the pattern A A C A A.
At this point, we have an array of A vectors (excluding blocks), blocks of A A C A A vectors, and B vectors.
Part 2: Resolving placement of B
The constraint on B is that two consecutive Bs must have at-least 2 non-B vectors between them.
Visualize as follows: Let's pool A and A A C A A in one array, X. Let's place all Bs in a row (suppose there are 3 Bs):
s0 B s1 B s2 B s3
Where s is the number of vectors between each B. Hence, we require that s1, s2 be at least 2, and overall s0 + s1 + s2 + s3 equal to number of vectors in X.
The task is then to choose random vectors from X and assign them to each s. At the end, we finally have a random vector with all categories shuffled, satisfying the constraints.
P.S. This can be mapped to the classic problem of finding a set of random numbers that add up to a certain sum, with constraints.
It is easier to reduce the constrained sum problem to one with no constraints. This can be done as:
s0 B s1 t1 B s2 t2 B s3
Where t1 and t2 are chosen from X just enough to satisfy constraints on B, and s0 + s1 + s2 + s3 equal to number of vectors in X not in t.
Implementation
Implementing the same in MATLAB could benefit from using cell arrays, and this algorithm for the random numbers of constant sum.
You would also need to maintain separate pools for each category, and keep building blocks and piece them together.
Really, this is not trivial but also not impossible. This is the approach you could try, if you want to step aside from brute-force search like you have tried before.
I hope you can help me with this one.
I am using cointegration to discover potential pairs trading opportunities within stocks and more precisely I am utilizing the Johansen trace test for only two stocks at a time.
I have several securities, but for each test I only test two at a time.
If two stocks are found to be cointegrated using the Johansen test, the idea is to define the spread as
beta' * p(t-1) - c
where beta'=[1 beta2] and p(t-1) is the (2x1) vector of the previous stock prices. Notice that I seek a normalized first coefficient of the cointegration vector. c is a constant which is allowed within the cointegration relationship.
I am using Matlab to run the tests (jcitest), but have also tried utilizing Eviews for comparison of results. The two programs yields the same.
When I run the test and find two stocks to be cointegrated, I usually get output like
beta_1 = 12.7290
beta_2 = -35.9655
c = 121.3422
Since I want a normalized first beta coefficient, I set beta1 = 1 and obtain
beta_2 = -35.9655/12.7290 = -2.8255
c =121.3422/12.7290 = 9.5327
I can then generate the spread as beta' * p(t-1) - c. When the spread gets sufficiently low, I buy 1 share of stock 1 and short beta_2 shares of stock 2 and vice versa when the spread gets high.
~~~~~~~~~~~~~~~~ The problem ~~~~~~~~~~~~~~~~~~~~~~~
Since I am testing an awful lot of stock pairs, I obtain a lot of output. Quite often, however, I receive output where the estimated beta_1 and beta_2 are of the same sign, e.g.
beta_1= -1.4
beta_2= -3.9
When I normalize these according to beta_1, I get:
beta_1 = 1
beta_2 = 2.728
The current pairs trading literature doesn't mention any cases where the betas are of the same sign - how should it be interpreted? Since this is pairs trading, I am supposed to long one stock and short the other when the spread deviates from its long run mean. However, when the betas are of the same sign, to me it seems that I should always go long/short in both at the same time? Is this the correct interpretation? Or should I modify the way in which I normalize the coefficients?
I could really use some help...
EXTRA QUESTION:
Under some of my tests, I reject both the hypothesis of r=0 cointegration relationships and r<=1 cointegration relationships. I find this very mysterious, as I am only considering two variables at a time, and there can, at maximum, only be r=1 cointegration relationship. Can anyone tell me what this means?
Say I give something like AB+AB+BA to matlab (or mupad), and ask it to simplify it. the answer should be: 2AB+BA. Can this be done in matlab or mupad?
Edit:
Ok, this is feeling rediculous. I'm trying to do this in either matlab or mulab, and.. it's frustrating not knowing how to do what should be the simplest things, and not being able to find the answers right away via google.
I want to expand the following, multiplied together, as a taylor series:
eq1 := exp(g*l*B):
eq2 := exp(l*A):
eq3 := exp((1-g)*l*B):
g is gamma, l is lambda (don't know how to represent either of these in matlab or mulab). A and B don't commute. I want to multiply the three exponentials together, expand, select all terms of a given power in lambda, and simplify the result. Is there a simple way to do this? or should I give up and go to another system, like maple?
This is mupad, not matlab:
operator("x", _vector_product, Binary, 1999):
A x B + A x B + B x A
returns
2 A x B + B x A
The vetor product is used, simply because it matches the described requirements.
I am wondering if there is some way, how to multiple assign values to different variables according logical vector.
For example:
I have variables a, b, c and logical vector l=[1 0 1] and vector with values v but just for a and c. Vector v is changing its dimension, but everytime, it has the same size as the number of true in l.
I would like to assign just new values for a and c but b must stay unchanged.
Any ideas? Maybe there is very trivial way but I didn't figure it out.
Thanks a lot.
I think your problem is, that you stored structured data in an unstructured way. You assume a b c to have a natural order, which is pretty obvious but not represented in your code.
Replacing a b c with a vector x makes it a really easy task.
x(l)=v(l);
Assuming you want to keep your variable names, the simplest possibility I know would be to write a function:
function varargout=update(l,v,varargin)
varargout=varargin;
l=logical(l);
varargout{l}=v(l);
end
Usage would be:
[a,b,c]=update(l,v,a,b,c)