Predicate logic and one point rule using Z notation

AI Thread Summary
The discussion revolves around the challenges of simplifying an equation using predicate logic and the one-point rule, with participants expressing confusion over specific notations like Z notation and the one-point rule. Many contributors note a lack of familiarity with Z notation, questioning its prevalence in university curricula despite its complexity. There is a call for standard notations in set theory and recommendations for resources to better understand these concepts. A participant suggests a specific book on Z notation as a helpful resource. Overall, the conversation highlights the need for clearer communication and resources in mathematical logic.
learn_maths
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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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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 \mathbb{N} 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.
 
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
 
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.
 
>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
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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