Predicate logic and one point rule using Z notation

In summary: I'll check it out. In summary, the author suggests using Z notation when dealing with sets and logic. However, he cautions that many people do not know what Z notation is and recommends starting a new thread if someone is interested in learning more.
  • #1
learn_maths
3
0
Hello all,

I'm in the process of simplifying the following equation using one-point rule and other predicate logic. But I’m a bit stuck with where to start or which inference rule to use first.

11053d1320180705-one-point-rule-127_8cd87652721067acc2f2a1af99d8b9db.png


Please help or any pointers would be much appreciated.

Thanks
 
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  • #2
learn_maths,

The notation and terminology of logic is not as standardized as the notation and terminology of a subject like Calculus. So if you ask a question about logic that uses a lot of notation, it is quite possible that people who did not study your particular textbook won't know what you're talking about.

Speaking for myself, I don't know what the "one point rule" is. I don't know what "Z notation" is. And I don't know what the [itex] \mathbb{N} [/itex] means in your formula. I presume it has to do with the natural numbers, but I don't see how it relates to any of the variables.
 
  • #3
Steve thanks for the reply. By far i have noticed that not many people know Z notation. And I’m quite surprised why then the universities prefer to use Z for teaching. Since I’m a learner what is the standard notation for set theory? Any links to understand the standard notation would be very helpful.

I did get same sort of reaction in few other forum when I posted Z notation.

Thanks
 
  • #4
I haven't opened a logic book in 30 years and I'm not current on good web sites for symbolic logic. If nobody else jumps into this thread with some recommendations, I'm sure that if you start a new thread whose title indicates you want links and books, you'll get some answers.

Do you have a good link or book for "Z notation"? I'm curious about it.
 
  • #5
>Do you have a good link or book for "Z notation"? I'm curious about it.
Check this book out. The title explains what the book is all about. This is the book which I'm referring at the movement.

http://www.cs.cmu.edu/~15819/zedbook.pdf

Thanks
 

Related to Predicate logic and one point rule using Z notation

1. What is predicate logic?

Predicate logic is a formal language used in mathematical and philosophical logic to represent relationships between objects and concepts. It uses logical symbols and quantifiers to express statements about the properties and characteristics of objects.

2. How is predicate logic used in Z notation?

Predicate logic is the foundation of Z notation, a formal specification language used in software engineering to describe and model systems. In Z notation, predicate logic is used to define data types, properties of data, and relationships between data objects.

3. What is the one point rule in Z notation?

The one point rule, also known as the unique existence rule, is a fundamental principle in Z notation. It states that for any given set, there can only be one element with a specific property or characteristic. This rule helps to ensure consistency and avoid ambiguity in Z notation specifications.

4. How is the one point rule applied in Z notation?

In Z notation, the one point rule is applied by using the unique existence quantifier, which is written as "!" followed by a variable and a predicate. This quantifier asserts that there exists exactly one element satisfying the given predicate within a given set.

5. What are the benefits of using Z notation and predicate logic?

Using Z notation and predicate logic allows for precise and unambiguous specifications of systems, making it easier to design, verify, and maintain software. It also helps to identify potential errors and inconsistencies in the early stages of system development.

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