For questions about artificial intelligence.

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4
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1answer
1k views

Convert a WFF to Clausal Form

I'm given the following question: Convert the following WFF into clausal form: \begin{equation*} \forall(X)(q(X)\to(\exists(Y)(\neg(p(X,Y)\vee r(X,Y))\to h(X,Y))\wedge f(X))) \end{equation*} ...
-3
votes
2answers
34 views

Simple ranking/rating algorithm [closed]

Is there a Simple ranking/rating algorithm that calculates a score between 0 and 1 given a number of alerts along with its priority. For example: each system can produce "Low", "Medium" and "High" ...
1
vote
1answer
26 views

Risk seeking utility

I am stuck on a question in an archived course on BerkeleyX's CS188x Artificial Intelligence. Which of the following would be a utility function for a risk-seeking preference? That is, for which ...
0
votes
0answers
11 views

Split a map into roughly equal sections directionally and put points in it

I have a 16000 x 9000 grid map and I want to split it into x sections that are preferably of equal size. Then I want to place points on each section are centers of circles with a 2200 unit radius and ...
1
vote
1answer
97 views

Contradiction in Davis–Putnam–Logemann–Loveland (DPLL) Method?!

As we see on page $10,11$ and $12$ on Google Books we know about Unit Clause (UC) and Pure Literal (PL) in DPLL Algorithms. in the following example if assign value $0$ to variables is prior to ...
0
votes
0answers
21 views

Is it better to average the log2 for a series of numbers or just the numbers themselves? And, how would you test or prove this?

Lets say I'm trying to compare two vectors for similarity and normalizing them before hand based on some mean or standard deviation combo for the purpose of finding the similarity between the 2 ...
1
vote
0answers
30 views

AI Parameters for Tetris-like Game

I am building an AI to play a variation of Tetris. The rules are changed in that there are 19 different types of pieces, rotation is not allowed, and the pieces can be placed anywhere in a 10X10 grid. ...
0
votes
0answers
19 views

Neural Networks: Solving XOR

A perceptron with two inputs $x_1$ and $x_2$ has following linear function and is hence able to solve linear separateable problems such as AND and OR. $f((x_1w_1+b)+(x_2w_2+b))$ $f(x)$ is the basic ...
2
votes
0answers
42 views

maximizing alpha-beta puning.

I was searching a more pertinent place to post artificial intelligence concerned question, but some results pointed me to similar questions posted here, thus I chose math.se, now let's get through ...
4
votes
2answers
80 views

Find sectors in a racing line.

Consider the following photo: To magnify image, right click and select open-image in new tab or something similar The photo above is a random race circuit data I've collected. What I'm trying to ...
0
votes
0answers
104 views

What kind of graph is the StackExchange?

Assuming that we have three distinct layers of nodes called Users, Questions & Answers, connected by the obvious way $(A)$, what kind of graph is the StackExchange? Do such graphs have special ...
0
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0answers
23 views

Boosting v. weighted average

I have been watching an MIT online Artificial Intelligence lecture by Prof. Winston about boosting. The boosting technique uses complicated maths to combine the results from several weak predictors to ...
3
votes
1answer
182 views

$i,j,k$ Values of the $\Theta$ Matrix in Neural Networks

SO I'm looking at these two neural networks and walking through how the $ijk$ values of $\Theta$ correspond to the layer, the node number. Either there are redundant values or I'm missing how the ...
3
votes
0answers
437 views

Modern Mathematical Theory for Neural Networks, Cellular Automata, Neuroscience

Is it possible for someone to do research on subjects like neural networks, cellular automata, or neuroscience as an applied mathematician? I have in mind the theoretical development of these fields,...
2
votes
1answer
1k views

What is the sigmoid *squashing* function?

I've just read the following The basic unit ("neuron" i) performs the following computation to update its state $y_i$: it computes a weighted sum $v_i$ of its inputs $x:j$ which is passed ...
1
vote
2answers
150 views

Memory of a neural network: is it forever?

As far as I remember a neural network cannot forget anything. Does this mean that no matters how evolved the network is, it's always going to throw me back the right output if I feed it an input? And ...
2
votes
0answers
86 views

How to Calculate Values from Incoming Messages? - Evidence Propagation in Bayesian Network

I'm currently trying to wrap my head around evidence propagation in bayesian network (simple tree propagation) but I'm having trouble finding information about the process. As an example, let's take ...
0
votes
0answers
35 views

How to calculate probabilities in a Bayesian network?

Consider the Bayesian network represented by the directed acyclic graph given below: We are given the following probabilities: P(tampering) = 0.02 P(fire) = 0.01 P(alarm | fire ∧tampering) = 0.5 ...
2
votes
1answer
44 views

What aspects of convex optimization are used in artificial intelligence, if any?

I work on convex optimization with Stephen Boyd's book. As an example, support vector machines are mentioned as an application of separating hyperplanes theorem. I am wondering if there is any other ...
-2
votes
1answer
76 views

Does this equation my professor wrote actually work? [closed]

Does this make sense to you? Peter's classroom example $\frac{1}{2^{(\text{any power})}} = \frac{1^{(\text{any power})}}{2^{(\text{any power})}} = (\frac{1}{2})^{(\text{any power})}$ If that's the ...
0
votes
0answers
9 views

How do I use resolution refutation in backward reasoning

Suppose I have the following facts in my KB: ∀a,b: g(a,b)→ p(a,b) ∀x: ¬p(x,x) ∀x,y,z: p(x,y)∧ p(y,z)→ p(x,z) ∀w,r: p(w,r)→ g(w,r) I have a questions: If I want ...
0
votes
1answer
36 views

Dung's Argumentation Framework

Given an extension of Dung's argumentation framework, and all definitions therein, let $$AF_1 = \langle A,Def \rangle$$ be a framework where $$A = \{ A, B, C, D, E, F, G, H \}$$ and $$Def = \{A def G, ...
0
votes
0answers
30 views

hamiltonian graph problem (sitting problem)

Hello guys sorry for noob question but i am learning graph theory and i am solving a question . in book it says it have only four solution but i founded that it can more than four so i am confused . ...
0
votes
0answers
66 views

The mathematics behind Google Deepmind

I'm aware of the following question: The mathematics behind AlphaGo AI and Google Deepmind I'm aware of math behind Perceptron and several other AI concepts: ...
1
vote
1answer
244 views

The mathematics behind AlphaGo AI and Google Deepmind [closed]

in case you are following the tech news, Google's AlphaGo beat the world Go champion Lee Sedol, not once but twice. Here is the link of the game 2 review: http://gogameguru.com/alphago-races-ahead-2-...
2
votes
1answer
41 views

Comparing two textbooks for machine learning

I am a Ph.D student in Electrical Engineering. I am going to study the field of machine learning and I found some textbooks to study this field. 1) Probabilistic Graphical Models: Principles and ...
0
votes
1answer
67 views

How to apply negation to a term?

EDIT: Maybe page 18 of this paper can help. This is a follow up from this question, where I am using ALCQ and I have this: $\lnot(3 \le \exists \text{hasPet}.\text{Animal})$ How to apply the ...
0
votes
1answer
20 views

Formulas of propositional logic, two sets and refutation.

Let $\alpha$ and $\beta$ be two formulas of propositional logic and set $S_\alpha$ and $S_\beta$ be the sets of clauses representing $\neg \alpha$ and $\neg \beta$, respectively. Show that if $S_\...
1
vote
1answer
25 views

How to find the optimal linear basis functions of an MDP?

Given a set of basis functions, there are many papers on finding a weight vector to linearly approximate the value function. Is there any paper on how to find the basis functions? Is it possible to ...
4
votes
1answer
176 views

State space for 8-queen problem

While reading Artificial Intelligence a Modern Approach I came across the following formulation for the 8-queen problem: Initial state: No queens on the board. States: Arrangements of n queens (0 &...
0
votes
1answer
47 views

Make individuals distinct

I am trying to construct an ALCQ knowledge base (KB) for some sentences. Here is what I have: Abox (Yiannis is a person and he drinks only one kind of a coffee, frappe): Person(YIANNIS) $\forall$ ...
0
votes
0answers
26 views

Use of activation derivative in back propagation algorithm

I'm a little confused how the activation derivative in back propagation work. Firstly, when I remove the activation derivative from the back propagation algorithm and replace it with a constant the ...
1
vote
2answers
117 views

Neural network cost function - why squared error?

Question: Why is the squared error most often used for training neural networks? Context: Neural networks are trained by adjusting the link weights. The key factor that informs these adjustments is ...
1
vote
1answer
57 views

LOGIC - Completeness vs Consistent

One of my exams questions were the following (translated from Hebrew) Course is in Artificial Intelligence, and is about Logic in this question. What is a consistent logic system? What is a ...
0
votes
1answer
27 views

who is lying? - by using Knowledge Base by resolution

I found this question online, and tryied to solve. However, I have trouble with the methods Here question Three children Allison, Jack, and Frank were playing “hide and seek” game in an apartment. ...
1
vote
0answers
26 views

The significance of odds and logs in Bayes Naive Classification

I do understand the concept of Naive Bayesian classification, as it tries to calculate the probability of an outcome of a class given multiple evidences. It comes from the Bayes theorem and it is ...
1
vote
0answers
39 views

Is normalized RBF always better than RBF

The question is as the title. Mathematically, I want to know does the following inequation always hold for any vector $\mathbf b$? $\mathbf b^T \mathbf B \mathbf B^+ \mathbf b \, \ge \, \mathbf b^T \...
1
vote
0answers
20 views

Implicit feature space of Power Kernel

For the polynomial kernel, $K(x,y) = (x^Ty+c)^d$, the implicit feature space $\phi$ for which $K(x,y) = \phi(x)^T \phi(y)$ is of finite dimension and well known [1][2]. It is also well known that the ...
0
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0answers
89 views

Solving differential equation using artificial intelligence

Hellow, I want to do my phd on the topics solving differential equation using artificial intelligence. At first I want to read some introductory books on artificial intelligence and then on the topic "...
0
votes
0answers
28 views

State space complexity of $2d$ and $3d$ tic tac toe

So for a 2d tic tac toe game, we know that the space complexity can be represented as follows. A naive upper bound will be $3^9$ as there is $3$ possibilities (X, Y or blank) in each of the $9$ ...
1
vote
0answers
38 views

Improving Simulated Annealing based on Measure of Goodness

can anyone answer this question or direct me to a reference that can help? Simulated Annealing returns the current state when the end of the annealing schedule is reached and if the annealing ...
0
votes
1answer
143 views

binary resolution rule proof

I want to proof the binary resolution rule that is, if we For any two clauses $C_1$ and $C_2$, if there is a literal $L_1$ in $C_1$ that is complementary to a literal $L_2$ in $C_2$, then delete $L_1$ ...
1
vote
0answers
48 views

Complexity analysis of alpha beta pruning of a full tree

I am trying to understand the derivation of a time complexity for an alpha-beta pruning algorithm but up till now have not found any reasonable recourse. Many recourses claim that if you take a full ...
0
votes
0answers
14 views

Using differential evolution to evaluate weights

I have an equation I am attempting to optimise of the form: w1x1 + w2x2 + w3x3 Using a pre defined fitness function. Unlike any of the original papers, I also have the constraint: Sum of the ...
0
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0answers
22 views

How does Best First Search Calculate the Heuristic Values in the Graph

I understand that Best First Search uses a sorted open list based on Heuristic Values of the Nodes (priority queue) and a closed list.But how are these Heuristic values of the Nodes calculated? The ...
0
votes
3answers
324 views

Reducing TIC-TAC TOE State Space by using Symmetry in Artificial Intelligence

Im learning Heuristics in AI.I see that for brute force search there are 9! states.But the textbook says that first 3 levels are reduced by symmetry.How does that work?
0
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0answers
15 views

What would linear neurons be able to model in artificial neural nets

Is it true that linear neurons are only useful in single layer neural nets because adding multiple layers will not allow the net to learn any interesting features because of the linear neurones?
0
votes
1answer
108 views

Math replacing natural language [closed]

Before reading any further. I ask yous to think creatively on this subject. I was in shower and was pondering over A.I. (Strong A.I. both at human level and beyond human level) as I do from time to ...
4
votes
2answers
96 views

Are there some functions that cannot be optimized using calculus?

I've been working on a project to maximize a functions output using a genetic algorithm. However, from the limited calculus I know I thought there were methods to find the maximum of a mathematical ...
0
votes
0answers
47 views

combine analysis and artificial intelligence

I'm sorry if I ask this question at the wrong place, but I don't know a better one. I am a Master's student and I am really interested in analysis, but I also want to get into AI. Does anyone know a ...