# Tag Info

### What is the correct way to use the implication in first-order logic?

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 ...
• 10.2k
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### What is a "closed expression" in the context of logic?

A closed expression (or closed formula) refers to a formula that 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 ...
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### Why do knowledge-based agents only add a sentence to the knowledge base when it is 100% sure the sentence is true?

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. ...
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### How would an AI work out this question?

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 "...
• 141
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### What is the meaning of the statement $\forall x \exists y \forall z (z \neq y \iff f(x) \neq z)$?

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 \...
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### Is randomness anti-logical?

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 ...
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### Is randomness anti-logical?

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 ...
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### Can (trained) neural networks be combined with symbolic AI to perform operations like AND?

I think you would be interested in Neural-Symbolic Learning and Reasoning, a recent survey on the intersection between connectionist models (e.g. neural nets) and symbolic reasoning. It's a long paper,...
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### Given statements $A$ and $B$, are the formulae $(\lnot A) \land (\lnot B)$ and $(\lnot A) \lor (\lnot B)$ equivalent?

One way of verifying whether two boolean expressions are equivalent is to assign all possibilities to all variables, and comparing all results. A B f1 f2 T T F F T F F T F T F T F F T T We can ...
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### Is logic AI a complement to learning AI?

What you refer to as logic AI is a subset of what is called symbolic AI, as you manipulate symbols, according to certain rules (which could be rules of logic). These rules are either authored by a ...
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### How can thought vectors be used outside of an Artificial Neural Network (ANN) context?

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 ...
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### What is the difference between logic-based and rule-based AI?

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, ...
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### Is there a system that automatically designs a set of rules from the examples?

This is an active research topic. Consider reading J.Pitrat's Artificial Beings, the conscience of a conscious machine book This Understanding machine learning book old Lenat's papers on Eurisko. ...

### Why is the Universal Declaration of Human Rights not included as statement on the AI?

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 ...
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### How to mathematically/logically represent the sense of sentences like "The cat drinks milk"?

Let start by classify the phrases you propose: The cat drinks milk. => action Sun is yellow. => descriptive/declarative, immutable I was at work yesterday. => descriptive, time related 1) The ...
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### How is uniqueness quantification translated in First Oder Logic

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 ...
• 5,397
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### When is a knowledge base consistent?

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 &...
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### When will we have computer programs that can compose mathematical proofs?

Arguably we have had this since 1957, with the General Problem Solver. However, it is a thorny problem, and like so much in AI, it works fine in toy domains (like the Towers of Hanoi problem), but ...
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### Can LLMs be used to discover new laws of logic?

In the quoted text, Stephen Wolfram uses scare quotes to signify loose, non-technical analogies. So by my reading, he is not claiming that ChatGPT has discovered any new type of logic. Instead he is ...
• 31.5k
1 vote

### What are the challenges faced by using NLP to convert mathematical texts into formal logic?

I can see several challenges, and the list below is not exhaustive: i. The main problem is how to model a problem of translating a language test into a formal language. It will probably be something ...
1 vote

### Is randomness anti-logical?

Let me add an example from machine learning that shows that resorting to randomness is the optimal way, sometimes. When working on the whole data is not tractable (computation cost, data does not ...
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1 vote

### Is randomness anti-logical?

Previous answers are very well written. I just wanted to supplement the thread by giving a simple example. The example shows how a logical function can be computed without errors using noisy ...
• 699
1 vote

### Is randomness anti-logical?

In certain games, random selection is the optimal strategy. See: Matching Pennies Strategy is essentially a plan of action utilized to achieve a goal. If random choice can be a strategy, it seems ...
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1 vote

### Why is description logic decidable but first order logic is not decidable?

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 ...
1 vote

### Possible to translate generic English-language document into higher-order logic?

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 ...
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1 vote

### Google's Principles of Artificial Intelligence

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 ...
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1 vote
Accepted

### Which edges of this tree will be pruned by Alpha-beta pruning?

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 ...
1 vote

### How to mathematically/logically represent the sense of sentences like "The cat drinks milk"?

People normally represent sentences like this as vectors of a specific length, normally about 2500 in length. The algorithm that can do this is sentence2vec. It is basically a derivative of word2vec. ...
1 vote

### String node untying algorithm

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 ...
1 vote

### What is meant by "known" in "A knowledge-base exhibits complete knowledge if and only if, for every $P$, $P$ or $\neg P$ is known"?

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 ...

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