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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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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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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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: ∃x.(house(x) ∧ In(x,area1) ∧ ∀y.(house(y) ∧ In(y,area1) ∧ size(y) < 200 -> x=y)) This…
xava
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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, you'll be annoyed. Does your dog mess up your…
Brat1097
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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 set of support and resolving one of elements in it first are helpful. But I cannot…
Maybe
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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 two clauses (where $A$ and $B$ are…
MikeKatz45
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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 value?
ammu
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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 undecidable?
shah
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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) Q →R v S 3) P → ~R This is from my reasoning…
user22282
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