# 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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### 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 ...
2k views

### 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 ...
624 views

### 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 ...
106 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 ...
48 views

### 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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### 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?
421 views

### 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 ...
82 views

### 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 ...
46 views

### 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....
11 views

### What are some good use cases of Inference in Hybrid Domains (Logical + Continuous)?

So this question pertains to Statistical Relational Learning. Specifically in domains where you have a Knowledge base with probabilistic facts, you may think something like a Markov Logic Networks (...
159 views

### 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 ...
370 views

### 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 ...
48 views

### 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 ...
26 views

### Can propositional resolution be done with DNF?

I have read that propositional resolution works best for formulas in CNF but does it also work with DNF? if yes how? if no why not?
123 views

### Can we optimize an optimization algorithm?

In this answer to the question Is an optimization algorithm equivalent to a neural network?, the author stated that, in theory, there is some recurrent neural network that implements a given ...
337 views

### 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. (...
76 views

### 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. ...
23 views

### 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 ...
105 views

### Meaning of the statement $\forall x \exists y \forall z (z \neq y \iff f(x) \neq z)$

I need to understand the logic of below FOL statement. Can someone help? $$\forall x \exists y \forall z (z \neq y \iff f(x) \neq z)$$ Does this imply that x, y and z cannot be same or f(x) has no ...
63 views

### 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 ...
84 views

### 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? ...
29 views

### 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 ...
123 views

### 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 ...
94 views

### 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 ...
78 views

### 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?
29 views

### 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 ...
66 views

### 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)...
762 views

### What does the term “closed expression” mean?

In the field of logic systems there is a property for reasoning algorithms called incompleteness or incompletion. In this context the phrase "any closed expression that is not derivable inside the ...
1k views

### 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, ...
51 views

### 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 ...
91 views

### AI Knowledge Based System: I am having difficulties understanding proposition logic

I am having difficulties wrapping my head around how the answer is being produced. How does the solution come up with the answer 3? How does one derive the answer 3 from the truth table? For example ...
136 views

### Google's Principles of Artificial Intelligence

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. ...
166 views

### Minimum number of perceptrons for an n-bit truth table?

Suppose I have a Boolean function that maps N bits to one bit. If I understand correctly, this function will have 2^2^N possible configurations of its truth table. What is the minimum number of ...
140 views

### 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 ...
56 views

### 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: ...
50 views

### 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 ...
94 views

### 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 ...
84 views

### 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 ...
299 views

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

Lots of people are afraid of what strong AI could mean for the human race. Some people wish for a sort of "Asimov law" included in the AI code, but maybe we could go a bit more far with the ...
80 views

### 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 ...
574 views

### Translate English Sentences into First-Order Logic without quantifiers

I have to translate the following English sentences into First-Order Logic without using quantifiers: ...