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7

Taken slightly out of order, let's address your three main questions: The logical inference in this question is flawed[?] I think that is the case here, although I think it is mainly the starting axioms, plus the assumption that there is a sound logical argument for The Singularity that can be attacked. I would take the position that there is no such ...


5

A closed expression refers to a formula which has no free variables [1]. This is also called sentence. In a logic system you have a set of axioms which are sentences and rules which state how to derive a sentence from this [2]. If a sentence can be derived from the axioms, this means that the axioms entail this sentence. If a sentence is not derivable, it is ...


4

I want to preface this by saying that the distinction is not clear. Nevertheless, I'll tell you what I know about this, and I will attempt to make the further clarification: The Structure of rule-based agents is: Take input from environment, pass through condition-based rules, and perform the action through actuators or anything which creates some ...


4

Mostly because traditional "knowledge based systems" are based purely on deductive logic and that's just the way deduction works. It only deals with what consequences must follow from the premises. Traditionally these systems didn't deal with probabilistic knowledge or other less strict forms of reasoning, like abduction. That said, it is possible to ...


4

I don't think that the "try all the numbers" approach is very representative, because I'm not sure whether or not the agent that uses that approach can be considered by any means AI. There is no "intelligence" in just checking numbers to try to prove the statement. An agent that is considered to be intelligent should apply a more intelligent approach. This ...


3

I will first recapitulate the key concepts which you need to know in order to understand the answer to your question (which will be very simple, because I will just try to clarify what is given as a "definition"). In logic, a formula is e.g. $f$, $\lnot f$, $f \land g$, where $f$ can be e.g. the proposition (or variable) "today it will rain". So, in a (...


3

The statement is "for all $x$, there exists a value of $y$ such that for all $z$, $z\neq y$ if and only if $z \neq f(x)$". This can be simplified: $$\begin{align} & & \forall x \exists y \forall z (z\neq y \iff z \neq f(x))\\ &\implies & \forall x \exists y \forall z (z=y \iff z = f(x))\\ &\implies & \forall x \exists y \forall z (...


3

Yes ... definitely. AI software should not be overly bound to tensors. The natural representation of a network is a network, not an array. Math Well Fitted for AI Vertices connected by directed edges is the closest mathematical equivalent to working nervous systems. Even the control circuit of a CPU, FPU, or GPU is a complex network of gates, not a grid ...


3

First, you need to consider what are the "parameters" of this "optimization algorithm" that you want to "optimize". Let's take the most simple case, a SGD without momentum. The update rule for this optimizer is: $$ w_{t+1} \leftarrow w_{t} - a \cdot \nabla_{w_{t}} J(w_t) = w_{t} - a \cdot g_t $$ where $w_t$ are the weights at iteration $t$, $J$ is the cost ...


3

I think the answer here lies in that the dictionary definition of randomness you have is not the one used in statistics, ML, or mathematics. We define randomness to mean there exists a distribution with generally greater than 0 uncertainty. Depending on who you talk to, we live in a random universe (the way we define quantum mechanics depends on a wave ...


3

I might misunderstand your question, but there seem to be different levels of logic at play here. Computing logic, whereby any computational process is based on processor logic. In this case, any computing is involving logic, as boolean logic drives any processing. Linguistic logic, where there is a logic in the sequencing of sentences within a text. A ...


2

I'll take a shot at answering this, though I'm no expert in Neural Nets or Deep Learning. Given that practical thought vectors (TVs) don't yet exist, and may be impractical or impossible, I think answering your question will require a lot of conjecture and speculation. So here goes... For thought vectors to be useful in or outside NNs, the vector values ...


2

According to the Wikipedia entry on Uniqueness Quantification your lecturer is correct. There is no size requirement expressed in the FOL expression. The point about the implication is that it can be true if the antecedent is false. So, there is a house in area1 (which we call x). And all houses in area1 which are smaller than 200 are the same as x. But if ...


2

The vanilla Alpha-Beta Pruning algorithm as it has been taught to you in class does not assume any domain knowledge / knowledge about the game / knowledge about the tree it is searching. Therefore, if it immediately finds a score of 10 directly to the left of the root node, it can not prune yet, because... maybe there's a score of 20 somewhere else in the ...


2

We usually optimize with respect to something. For example, you can train a neural network to locate cats in an image. This operation of locating cats in an image can be thought of as a function: given an image, a neural network can be trained to return the position of the cat in the image. In this sense, we can optimize a neural network with respect to this ...


2

Some of the work on descriptive logics and modal logics was done within the context of artificial intelligence from a research funding perspective. Some was part of the normal academic apparatus of mathematics departments. Furtherance of these fields in the AI context has been hindered by historically low return on investment. Although first order logic, ...


2

When we state in English that "All As are Bs", this means that we gain information as soon as we observe an A, we can immediately deduce that it must also be a B. These are the kinds of situations where we use an implication. So, this would be written in formal logic as: $$\forall X \left( A(X) \rightarrow B(X) \right)$$ When we state in English that "Some ...


2

If I understand what you are asking, I think the simple answer would be that AI is nowhere near having demonstrated sentience, thus they do not qualify for any type of rights. We won't have to "cross this bridge" until an AI demonstrates self-awareness and human-level-or-beyond intelligence, but it sure is interesting to think about! (Also, the UDHR dates ...


1

This has to do with the fact that you can define arithmetic inside the axiomatic system or not. In description logic you cannot speak about arithmetic sentences and in first order logic you do. if you look at the proof of incompleteness you will understand this in depth. This demonstration depends on an arithmetic coding of statements, and this ...


1

There are several problems with this, which is why people have been working on tasks like that for about 50 years without getting very far. As you rightly notice, it has been tried in restricted domains, where it works reasonably well. Reason being, there is less ambiguity. Human language is full of vagueness and ambiguity. We generally have few problems ...


1

In computers, where everything derives from mathematics, I think a rule is nothing but a function which is approximated by analysing the relationship between the input and output. Suppose we are training a Convolutional neural network, we give it some images as input and an Integer number ( Ex.1 ) as the output. The network's job is to find a function which ...


1

Artificial Intelligence at Google — Our Principles Objectives for AI Applications Be socially beneficial. Avoid creating or reinforcing unfair bias. Be built and tested for safety. Be accountable to people. Incorporate privacy design principles. Uphold high standards of scientific excellence. Be made available for uses that accord with these ...


1

This is a homework for first order logic. The task itself is easy. Only the third point on the list “prove by contradiction” is a bit more difficult to interpret, as the term prove is not defined exactly in a mathematical context. In the domain of game theory, to prove something means to find a walk-through for the game. If something was proven, a plan was ...


1

The provided result is a non-sense for this input. In a closed world paradigm (ie: prolog), where all non-provable facts are assumed as false, from "p2->p3 and p3->p1", p2 is false, and the program result should be "p2 ? No". In an open world, as it is not possible to proof "p2" nor "not p2", the result must be "p2 ? unknown" "p2 -> p3 and p3 -> p1" doesn'...


1

If you prune k and L then you could miss the optimal solution. Assume L=9, if you prune L then the value of the tree is 8. If you don't prune L then the value of the tree is 9. Now I will try and address what I think your actual question is But no matter what, the decision of the max(root) will not change, the max will choose the right side no matter what ...


1

This is a very dicey question. Logic functions can be thought of as mapping multiple inputs to a single output. Now each logic function create its own boundary. So if you are using a complex logical equation it is actually very hard to approximate the underlying function. Here I am treating the input Booleans as the input features. From practical experience:...


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Sequential programming would not be suitable for this kind of problem, but an algorithm could be implemented in a declarative programming language. I would suggest using Answer Set Programming, a language that is designed for logic axioms.


1

http://inst.eecs.berkeley.edu/~cs61b/fa14/ta-materials/apps/ab_tree_practice/ you can make practice for better understanding the topic. And i also recommend this lecture from MIT https://www.youtube.com/watch?v=STjW3eH0Cik&index=6&list=PLUl4u3cNGP63gFHB6xb-kVBiQHYe_4hSi


1

Rule-based systems cover a wide range of systems. Some make use of boolean if/then/else rules, others may use weighting or even probabilistic inference. Some operate on frames, some on java objects, some on propositions that can be formulated in predicate logic. An example of a popular rule system is Drools. Some rule systems can be expressed as a subset of ...


1

It seems that they are stating that a knowledge base is consistent if and only if it never asserts the truth of both the truth and the negation of a particular P. In other words, a knowledge base is consistent if it never contradicts itself. Their definition allows incomplete knowledge bases to be considered consistent; by their definition, an empty ...


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