<p>It depends what precisely do you want to learn. A good reference is the finite model theory book by Libkin. <a href="https://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf" rel="nofollow noreferrer">https://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf</a> (chapters 2 and 7).</p>
<p>If you want more specific references, please be more precise with your question.</p>

CC BY-SA 4.0
2023-01-05T12:37:56.233Z
Thanks for the answer. First, I would like to become familiar with the definitions and theorems of FO and MSO, although not on an advanced level. Furthermore, I am interested in knowing what problems and properties in graph theory are expressed and cannot be expressed by FO and MSO.
fva
CC BY-SA 4.0
2023-01-05T14:01:41.647Z
Ok, so I think that the first two chapters would be ok of Libkin's book will be ok (+ the chapter about MSO). Otherwise, you can also go through the following undergrad book: Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics) https://www.amazon.com/Mathematical-Logic-Undergraduate-Texts-Mathematics/dp/0387942580
Bartosz Bednarczyk
CC BY-SA 4.0
2023-01-06T16:10:58.580Z
Thanks! It seems like a great book. The book "Graph Structure and Monadic Second-Orderer Logic" by Courcelle and Engelfriet was also recommended by a friend.
fva
CC BY-SA 4.0
2023-01-06T18:46:00.200Z
Yes, but this is a way more advanced than the ones that I told you (say,  undergrad level vs PHD student / researcher level).
Bartosz Bednarczyk
CC BY-SA 4.0
2023-01-05T11:40:02.587Z
2023-01-05T11:40:02.587Z
Bartosz Bednarczyk
<p>What are some good books and surveys for learning about first-order logic and monadic second-order logic?</p>
<p>I'm a graduate student in computer science with a focus on algorithms. For model-checking on graphs, I need to be familiar with the FO and MSO logics.</p>

<graph-algorithms><lo.logic><model-checking><first-order-logic>
Resources for first-order and second-order monadic logics with a model-checking objective
fva
# Resources for first-order and second-order monadic logics with a model-checking objective

(Asked by: username_0 on 2023-01-05)

What are some good books and surveys for learning about first-order logic and monadic second-order logic?

I'm a graduate student in computer science with a focus on algorithms. For model-checking on graphs, I need to be familiar with the FO and MSO logics.

**Tags:** graph-algorithms, lo.logic, model-checking, first-order-logic

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## 1 answers

### Answer by username_1 on 2023-01-05. Score: 4 | Accepted answer

It depends what precisely do you want to learn. A good reference is the finite model theory book by Libkin. <https://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf> (chapters 2 and 7).

If you want more specific references, please be more precise with your question.

> **Comments:**
> **username_0**: Thanks for the answer. First, I would like to become familiar with the definitions and theorems of FO and MSO, although not on an advanced level. Furthermore, I am interested in knowing what problems and properties in graph theory are expressed and cannot be expressed by FO and MSO.  
> **username_1**: Ok, so I think that the first two chapters would be ok of Libkin's book will be ok (+ the chapter about MSO). Otherwise, you can also go through the following undergrad book: Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics) https://www.amazon.com/Mathematical-Logic-Undergraduate-Texts-Mathematics/dp/0387942580  
> **username_0**: Thanks! It seems like a great book. The book "Graph Structure and Monadic Second-Orderer Logic" by Courcelle and Engelfriet was also recommended by a friend.  
> **username_1**: Yes, but this is a way more advanced than the ones that I told you (say,  undergrad level vs PHD student / researcher level).  

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