Questions tagged [logic]

For questions about algorithms and concepts for the development or use of logical inference capabilities in computers or the use of logical inference to arrive at the most useful AI designs.

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What is the "state of the art" in (at least partially) symbolic/logic-based chat bots/AI assistants?

ChatGPT has had a lot of buzz around it recently, and for good reason. It has shown some amazing capabilities in responding to new information, as well as in generalizing new information that has been ...
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How to relate the definition for entailment, with soundness and completeness?

Is it fair enough to say for a language model, φ, which makes certain variable A true, and if φ also makes another variable B true, then we can conclude: A ⊨ B And for a certain inference calculus c,...
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1 answer
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Can the truth value of unobserved sentences be computed from known sentences only?

Truthfulness is a quality that Sam Altman mentioned to be improvable on ChatGPT. This question considers a small example to try to understand the problem. A large language model includes a large set ...
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1 answer
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Are my attempts to write "There exists a student studying all the subjects of the information technology subject" in FOL correct? [closed]

I have the following sentence, which I need to write in FOL There exists a student studying all the subjects of the information technology subject I don't know how $\forall$ can be combined with the ...
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Consider the following axioms- [closed]

I'm studying Artificial Intelligence and I have a question about first order logic and resolution. But I couldn't find any answer why. I tried using Google to get the answer but nothing was found.
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How is forward chaining complete?

Can anyone explain why forward chaining is complete? The AIMA proof went over my head. I understood the working of the algorithm and how we finally have an inferred ...
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AIMA, Inference Algorithm - Sound or Truth Preserving

AIMA: Chapter 7, page 216, Global Edition. An inference algorithm that derives only entailed sentences is called sound or truth preserving. Soundness is a highly desirable property. An unsound ...
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1 vote
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How to represent multiple-output logic circuits in tree-based genetic programming

Consider the following digital logic circuit, which has multiple inputs and one output: The logic circuit above can be represented in tree form: This tree representation could then be used in a tree-...
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1 answer
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Is logic AI a complement to learning AI?

I want to know the relation between logic AI and learning AI. Logic AI here refers to the branch of AI that is based on mathematical logic. Learning AI refers to the branch of AI that is based on ...
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How do I show the relationship between theories and models using Conceptual Graphs?

The Mereology Theory below contains three first-order axioms that represent a part of a mereology theory. For this posting, it is important that the set of axioms should be considered as a theory. ...
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Why is BERT/GPT capable of "for-all" generalization?

As shown in the figure: Why does token prediction work when "Socrates" is replaced with "Plato"? From the point of view of symbolic logic, the above example effectively performs ...
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How are theories represented using Conceptual Graphs?

Theory 1 shows three axioms and two definitions, written in First Order Logic (FOL), that represents a fragment of a mereology theory. For this posting, it is important that the set of axioms is ...
1 vote
1 answer
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What is the difference between "Syllogism" and "Law of Syllogism"?

The logical arguments are the basis for Artificial Intelligence. That is why I picked AI community to ask my question. Reading from Wikipedia, A syllogism is a kind of logical argument that applies ...
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Do these FOL formula both represent "You can fool some of the people all of the time"?

You can fool some of the people all of the time. This can be represented in FOL as follows $$\exists x \; \forall t \; (\text{person}(x) \land \text{time}(t)) \Rightarrow \text{can-fool}(x,t) \tag{1}...
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1 answer
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How to translate sudoku XV boards in CNF format?

I'm trying to implement the logic for a Sudoku XV puzzle, that it's essentially a standard sudoku with the addition of X and V markers between some pairs of squares. X markers in adjacent pairs ...
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858 views

What is the difference between derivation and entailment?

In section 7.3 of the book Artificial Intelligence: A Modern Approach (3rd edition), it's written An inference algorithm that derives only entailed sentences is called sound or truth-preserving. The ...
1 vote
1 answer
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When to use AND and when to use Implies in first-order logic?

I am trying to learn the theory behind first-order logic (FOL) and do some practice runs of converting statements into the form of FOL. One issue I keep running into is hesitating on whether to use an ...
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What are the challenges faced by using NLP to convert mathematical texts into formal logic?

From what I've figured (a) converting mathematical theorems and proofs from English to formal logic is a straightforward job for mathematicians with sufficient background, except that it takes time. ...
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Implementing Logic Inference with Deep Learning

Short question How can I implement Logic Inference with Deep Learning? Long question Based on Symbolic Logic, chaining multiple predicates (a short example is Syllogism) is a method of implementing ...
1 vote
1 answer
106 views

Does the substituted variable/constant have to appear in the unified term?

I'm checking out how to manually apply resolution on a first order predicate logic knowledge base and I'm confused about what is allowed or not in the algorithm. Let's say that we have the following ...
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Developmental systems that try to explain or understand the reward value in the reinforcement learning?

Are there methods (possibly logical or (how they are called in the literature) relational) that allows for the developmental systems to understand or explain the value of the received reward during ...
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Is randomness anti-logical?

I came across a comment recently "reads like sentences strung together with no logic." But is this even possible? Sentences can be strung together randomly if the selection process is random. (...
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4 votes
1 answer
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How would an AI work out this question?

I am trying to create an AI that makes reasonable guesses at truths of statements. However... Human: "Prove that no number exists which is one more than a billion." AI: "Is it true for the number 1? ...
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Formulation of a sentence using FOL

I want to formulate the following sentence using FOL; I want also to know whether there any contradictions in it, or if it is consistent. Assuming human relations are binary: All Human Relations ...
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What is the meaning of the statement $\forall x \exists y \forall z (z \neq y \iff f(x) \neq z)$?

I need to understand the meaning of the FOL statement below. $$ \forall x \exists y \forall z (z \neq y \iff f(x) \neq z) $$ Does this imply that $x$, $y$, and $z$ cannot be the same or $f(x)$ has no ...
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Why is description logic decidable but first order logic is not decidable?

Description logic is a fragment of first order logic, but description logic is decidable and first order logic not decidable. Why is that? what is the role of variables in first order logic to make it ...
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Can (trained) neural networks be combined with symbolic AI to perform operations like AND?

Does anyone work out ways of relating trained neural networks by symbolic AI? For example, if I train a network on pictures of dogs, and I train a network on pictures of shirts. You could imagine that ...
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Logic questions: reasoning pattern, Infer literals, unit resolution, and-elimination etc

Show which literals can be inferred from the following knowledge bases, using both reasoning patterns and truth tables. Show all steps in your reasoning and explain your answers. 1) P & Q 2)...
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When is a knowledge base consistent?

I am studying a knowledge base (KB) from the book "Artificial Intelligence: A Modern Approach" (by Stuart Russell and Peter Norvig) and from this series of slides. A formula is satisfiable ...
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Choice of fuzzification function

I'm a relative newbie to fuzzie logic systems but I have some knowledge in mathematics. I have the following problem: I want to fuzzify certain values. Some are in the range [-$\inf$,$\inf$] and some ...
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1 answer
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When will we have computer programs that can compose mathematical proofs?

When will it be possible to give a computer program a bunch of assumptions and ask it if a certain statement is true or false, giving a proof or a counterexample respectively?
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1 answer
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Possible to translate generic English-language document into higher-order logic?

(Un-original) idea: Wouldn't it be cool if we could fact-check using an algorithm that could understand a whole bunch of documents (e.g. scientific papers) as higher-order logic? Question: What work ...
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6 votes
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What are the current trends/open questions in logics for knowledge representation?

What are the future prospects in near future from a theoretical investigation of description logics, and modal logics in the context of artificial intelligence research?
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How do I use truth tables to prove Entailment?

For example, consider an agent concerned with predicting the weather, with variable R indicating whether or not it is likely to rain, variable C indicating whether or not it is cloudy, and variable L ...
3 votes
1 answer
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What is the correct way to use the implication in first-order logic?

I know the implication symbol, $\rightarrow$, is used for conditions like If $A$ is true, then $B$ will be true. which can be written as $$ A \rightarrow B $$ However, sometimes the implication ...
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1 answer
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Google's Principles of Artificial Intelligence [closed]

Earlier this month, Google released a set of principles governing their AI development initiatives. The stated principles are: Objectives for AI Applications: Be socially beneficial. ...
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1 vote
1 answer
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How is uniqueness quantification translated in First Oder Logic

I have this following natural language statement: "There is only one house in area1 the size of which is less than 200m²." which is mistranslated to FOL: ...
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1 vote
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Which edges of this tree will be pruned by Alpha-beta pruning?

So I know that 'h' and 'f' will be pruned, but I'm not sure about 'k' and 'l'. When we visit 'j', technically there is no need for us to visit 'k' and 'l' because there are 2 options: one or two of ...
2 votes
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86 views

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

I am absolutely new in the AI area. I would like to know how to mathematically/logically represent the sense of sentences like: The cat drinks milk. Sun is yellow. I was at work yesterday. So, that ...
1 vote
2 answers
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String node untying algorithm

Let say that we have four straight string with colors RED, GREEN, BLUE and YELLOW. These strings are tied up randomly. We know the current state of string (like starting point, where we should we ...
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Writing a knowledge base (KB) in propositional logic and converting the KB into conjunctive normal form

If you walk your dog, he'll be happy. If you don't walk him, he'll chew up your furniture. If he's happy or if he chews your furniture, he'll mess up your apartment. If he messes up your apartment, ...
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Is there a system that automatically designs a set of rules from the examples?

Being by no means an expert in the field, I do however know of solvers such as Z3 that can generate a correct program, provided you can express your constraints as a set of logical rules, such as here....
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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?

According to Russell and Norvig, a knowledge-based agent will only add a sentence to its knowledge base if it follows logically from what it previously knows, or directly observes. To follow logically ...
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Answer Set Programming - Make a Fact INVALID

I have a question regarding Answer Set Programming on how to make an existing fact invalid, when there is already (also) a default statement present in the Knowledge Base. For example, there are two ...
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8 votes
1 answer
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What is the difference between logic-based and rule-based AI?

I always thought rule-based was synonymous with logic-based AI. Logic has axioms and rules of inference, whereas rule-based AI has a knowledge base (essentially, axioms) and if-then rules to create ...
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How to select the set of support and why?

In Artificial Intelligence: a Modern Approach, when it talks about strategies to improve efficiency of resolution inference(section 9.5.6), it says selecting the ...
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8 votes
3 answers
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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"?

I have a question as to what it means for a knowledge-base to be consistent and complete. I've been looking into non-monotonic logic and different formalisms for it from the book "Knowledge ...
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1 answer
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What are examples of AI that use philosophy derived ontologies?

I'm looking for AI systems or natural language processors that use, in the classification and interrelation of notions/objects, some philosophical system, like basic laws of logic, Kantian or ...
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2 votes
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How do I translate these English sentences into first-order logic without quantifiers?

I have to translate the following English sentences into First-Order Logic without using quantifiers: Everyone on flight 815 has a story. No one knows what is inside the hatch. Someone on the island ...
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Given statements $A$ and $B$, are the formulae $(\lnot A) \land (\lnot B)$ and $(\lnot A) \lor (\lnot B)$ equivalent?

If I have 2 statements, say $A$ and $B$, from which I formed 2 formulae: $f_1: (\lnot A) \land (\lnot B)$ $f_2: (\lnot A) \lor (\lnot B)$ Are $f_1$ and $f_2$ equivalent?
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