Convert statements into first order logic

Thread starter Marclan
Start date Jan 6, 2017
Tags

Convert First order First order logic Logic

In summary: I'm trying to solve only the problem posted above for now.i = ∀x ∀y (member(x) ∧ bicycle(y) ∧ owns(x,y) ∧ ∃ z brand(y,z) → ¬∃ z2 brand(y,z2))This statement is saying that for every member x and every bicycle y owned by that member, there exists a brand z such that the bicycle y has that brand. Then, it says that there does not exist another brand z2 for that bicycle y. This does not match the meaning of the statement given in the problem.The correct statement for i) would be:∀x ∀y ∀z (member(x) ∧ bicycle(y) ∧ owns(x,y) ∧ brand(y,z) →

Jan 10, 2017

PeroK

Science Advisor

Homework Helper

Insights Author

Gold Member

2023 Award

Marclan said:

iii) ∃z ∀x ∃y (member(x) ∧ bicycle(y) ∧ owns(x,y) ∧ brand(y,z) → ∀x2 ∃y2 (member(x2) ∧ bicycle(y2) ∧ owns(x2,y2) ∧ brand(y2,z)))

So, can i mark this thread as finally solved?

The qualifiers at the beginning were key. Once you get those in the correct order, it's just:

∃z ∀x ∃y (member(x) ∧ bicycle(y) ∧ owns(x,y) ∧ brand(y,z))

<h2> What is first order logic?</h2><p>First order logic is a formal language used in mathematical logic and computer science to represent and reason about statements or propositions. It is also known as first-order predicate calculus or first-order predicate logic.</p><h2> How do you convert statements into first order logic?</h2><p>To convert statements into first order logic, you need to identify the objects, predicates, and quantifiers present in the statement. Then, you can use symbols and logical connectives to represent these elements and create a logical formula that accurately captures the meaning of the original statement.</p><h2> What are the benefits of using first order logic?</h2><p>First order logic allows for precise and unambiguous representation of statements, making it easier to reason about them. It also allows for the use of logical rules and inference to derive new conclusions from existing statements. Additionally, first order logic is the foundation for many automated reasoning and artificial intelligence systems.</p><h2> Are there limitations to first order logic?</h2><p>Yes, there are limitations to first order logic. For example, it cannot capture certain types of statements that involve modalities, such as "necessarily" or "possibly." It also cannot handle self-referential statements or statements involving infinite sets. Higher-order logics have been developed to address some of these limitations.</p><h2> Can first order logic be used in everyday life?</h2><p>While first order logic is primarily used in formal settings such as mathematics and computer science, its principles can also be applied to everyday life. For example, it can help with critical thinking and evaluating arguments, as well as in decision making and problem solving. However, it may not always be necessary or practical to use first order logic in everyday situations.</p>

FAQ: Convert statements into first order logic

What is first order logic?

First order logic is a formal language used in mathematical logic and computer science to represent and reason about statements or propositions. It is also known as first-order predicate calculus or first-order predicate logic.

How do you convert statements into first order logic?

To convert statements into first order logic, you need to identify the objects, predicates, and quantifiers present in the statement. Then, you can use symbols and logical connectives to represent these elements and create a logical formula that accurately captures the meaning of the original statement.

What are the benefits of using first order logic?

First order logic allows for precise and unambiguous representation of statements, making it easier to reason about them. It also allows for the use of logical rules and inference to derive new conclusions from existing statements. Additionally, first order logic is the foundation for many automated reasoning and artificial intelligence systems.

Are there limitations to first order logic?

Yes, there are limitations to first order logic. For example, it cannot capture certain types of statements that involve modalities, such as "necessarily" or "possibly." It also cannot handle self-referential statements or statements involving infinite sets. Higher-order logics have been developed to address some of these limitations.

Can first order logic be used in everyday life?

While first order logic is primarily used in formal settings such as mathematics and computer science, its principles can also be applied to everyday life. For example, it can help with critical thinking and evaluating arguments, as well as in decision making and problem solving. However, it may not always be necessary or practical to use first order logic in everyday situations.