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.

Theoretical computer science developed out of logic, the theory of computation (if this is to be considered a different subject from logic), and some related areas of mathematics. So theoretically minded computer scientists are well informed about logic even when they aren't logicians. Computer scientists in general are familiar with the idea that logic provides techniques for analyzing the inferential properties of languages, and with the distinction between a high-level logical analysis of a reasoning problem and its implementations. Logic, for instance, can provide a specification for a programming language by characterizing a mapping from programs to the computations that they license. A compiler that implements the language can be incomplete, or even unsound, as long as in some sense it approximates the logical specification. This makes it possible for the involvement of logic in AI applications to vary from relatively weak uses in which the logic informs the implementation process with analytic insights, to strong uses in which the implementation algorithm can be shown to be sound and complete. In some cases, a working system is inspired by ideas from logic, but acquires features that at first seem logically problematic but can later be explained by developing new ideas in logical theory. This sort of thing has happened, for instance, in logic programming.

Logic and AI - Stanford Encyclopedia

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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?
mfioah
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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 new knowledge (essentially inference rules). But in…
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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 Representation and Reasoning" by Hector Levesque and Ronald…
Parry
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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. (Random sentences in a random sequence.) Stochasticity…
DukeZhou
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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 essentially means that if the premises are true,…
Peter
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What is a "closed expression" in the context of logic?

I was reading about logic systems and the following phrase appeared. any closed expression that is not derivable inside the same system What is a "closed expression" in this context? What does "closed expression that is not derivable" mean?
Ale
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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 the simplest way (without going through the…
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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 if there is some assignment to the variables that makes the…
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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?
Coder
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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? No. I am 1% sure the statement is correct." AI:…
zooby
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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 indicating low pressure. Given knowledge base…
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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 symbol is also used in other contexts. For example,…
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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 given to it. However, ChatGPT also regularly…
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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 persons seby and andy, one of them is able to…
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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 empiricism. I have also read about goal-seeking…
user5977
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