<p><code>Answer to A.</code> Barwise &amp; Etchemendy's <a href="http://rads.stackoverflow.com/amzn/click/1575866323" rel="nofollow">Language, Proof, and Logic</a> is a decent introduction to logic. From the perspective of someone coming from a CS background I found it especially accessible and fun. It's very clearly written, has lots of examples, and comes with 3 programs: </p>

<blockquote>
  <ol>
  <li><em>Tarski's World</em>: is a block world where you can verify the truths of sentences or find counterexamples in an intuitive, visual environment<br></li>
  <li><em>Fitch</em>: is a Fitch-style proof system that will check your proofs<br></li>
  <li><em>Boole</em>: is a truth-table tool</li>
  </ol>
</blockquote>

<p>Once you're done with the main course (I-II), in part III they have more fun topics to explore:</p>

<blockquote>
  <ol>
  <li><em>ZFC</em></li>
  <li><em>program correctness</em></li>
  <li><em>resolution</em></li>
  <li><em>Skolemization</em></li>
  <li><em>metalogic</em> (e.g. Lowenheim-Skolem, Compactness, Incompleteness) </li>
  </ol>
</blockquote>

<p>As I said, B &amp; E is an introductory course, so next you can move to what's called <em>mathematical logic</em>, which is more technical but more precise and will turn out to be more rewarding in the long run. A canonical text here is Enderton's <a href="http://rads.stackoverflow.com/amzn/click/0122384520" rel="nofollow">A Mathematical Introduction to Logic</a>, which even has a special chapter dedicated to <em>Second-Order Logic</em> (something you said you're interested in). It's not as interactive as B &amp; E, but it's a classic and it will prepare you for more advanced logic.</p>

<p><code>Answer to B.</code> How to give the semantics of operators should become clear after studying these texts. But if you're looking for special kinds of semantics, such as Kripke,  topological, neighborhood, measure-theoretic, domain-theoretic, probabilistic, etc., you'll have to do a little digging to find papers that explain how these things are done.</p>

<p>Hope that addresses at least some of your questions.</p>

CC BY-SA 3.0
2013-08-16T16:35:05.250Z
2013-08-16T18:06:07.987Z
2013-08-16T18:06:07.987Z
Hunan Rostomyan
<p>I am working on a project that requires me to learn about logic (specially first order and second order).</p>

<p>Looking for a good book or online reference that can help me with questions such as:</p>

<p>A. What is the difference between Logic, Language and Calculus?</p>

<p>B. How to define operators and their semantics?</p>

<p>etc.</p>

<p>As a beginner, it would be great to read a step by step like instructions with easy examples that helps me understand and build on.</p>

<p>Thanks in advance
Karl</p>

<reference-request><lo.logic>
Logic, language, semantics and more
Karl 17302
# Logic, language, semantics and more

(Asked by: username_0 on 2013-08-16)

I am working on a project that requires me to learn about logic (specially first order and second order).

Looking for a good book or online reference that can help me with questions such as:

A. What is the difference between Logic, Language and Calculus?

B. How to define operators and their semantics?

etc.

As a beginner, it would be great to read a step by step like instructions with easy examples that helps me understand and build on.

Thanks in advance
Karl

**Tags:** reference-request, lo.logic

---

## 1 answers

### Answer by username_1 on 2013-08-16. Score: 2 | Accepted answer

`Answer to A.` Barwise & Etchemendy's [Language, Proof, and Logic](http://rads.stackoverflow.com/amzn/click/1575866323) is a decent introduction to logic. From the perspective of someone coming from a CS background I found it especially accessible and fun. It's very clearly written, has lots of examples, and comes with 3 programs:

> 1. *Tarski's World*: is a block world where you can verify the truths of sentences or find counterexamples in an intuitive, visual environment
> 2. *Fitch*: is a Fitch-style proof system that will check your proofs
> 3. *Boole*: is a truth-table tool

Once you're done with the main course (I-II), in part III they have more fun topics to explore:

> 1. *ZFC*
> 2. *program correctness*
> 3. *resolution*
> 4. *Skolemization*
> 5. *metalogic* (e.g. Lowenheim-Skolem, Compactness, Incompleteness)

As I said, B & E is an introductory course, so next you can move to what's called *mathematical logic*, which is more technical but more precise and will turn out to be more rewarding in the long run. A canonical text here is Enderton's [A Mathematical Introduction to Logic](http://rads.stackoverflow.com/amzn/click/0122384520), which even has a special chapter dedicated to *Second-Order Logic* (something you said you're interested in). It's not as interactive as B & E, but it's a classic and it will prepare you for more advanced logic.

`Answer to B.` How to give the semantics of operators should become clear after studying these texts. But if you're looking for special kinds of semantics, such as Kripke, topological, neighborhood, measure-theoretic, domain-theoretic, probabilistic, etc., you'll have to do a little digging to find papers that explain how these things are done.

Hope that addresses at least some of your questions.


---

