Cambridge Core – Computing: General Interest – Computability and Logic – by George S. Boolos. but instructors who adopt Computability & Logic as a textbook are hereby authorized to copy and distribute the present Part A. This permission does not extend. Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the.
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Craig’s interpolation theorem lets us construct a sentence that is “between” an implication and has some nice properties.
Book Review: Computability and Logic
Still the best introduction to advanced logic and metatheory. It turns out Turing programs are enumerable as is anything you can write out with symbols from a finite alphabet.
This chapter introduces the syntax of first order logic. Sets and relations are called “primitive recursive” if their indicator functions can be constructed from primitive recursive building blocks.
Thomas Schminke rated it really liked it Oct 22, It feels a little easy, but that’s not a bad thing. Rajeev Shrivastava rated it it was amazing Jan 13, Again, this chapter is clever and fun to read. This is a result that’s assumed in many other texts “and, by diagonalization, we can construct…”but rarely explored in full.
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem.
Jul 14, Adam rated it it was amazing Shelves: Not the best written book. But if the theorem has always seemed somewhat confusing to you even after the cartoon guide then this chapter may well be enlightening. This is all well and good, but I was expecting much more detail and motivation, given the impressive motivation found elsewhere in the book.
That said, I didn’t find it very useful to me personally. Apr 26, Micah added it Shelves: The chapter walks you through the whole thing and makes it easy. This is interesting, because it shows us precisely where undecidability sets in. To ask other readers questions about Computability and Logicplease sign up. Jun 22, Warunika Ranaweera rated it it was amazing.
The FOL chapters could have done with some rework. Cristian CaludeM. This chapter introduces Turing Computability, which is literally the bedrock of computer science. There is No Paradox of Logical Validity.
Computability and Logic
This chapter is perhaps less fun than the others, but no less important. For those of you who don’t know, the Turing Machine is an idealized loigc engine which can compute answers to a very large class of problems. After putting down Model Theory partway through I picked up a book on logic.
This book excels at showing you the actual mechanisms behind results that are often mentioned but seldom exposed.
Read it if you’re curious, skip it if you’re not. Or you can decide to work without function symbols, and so on. Emily rated it really liked it Sep 18, There was one every few chapters. It’s very interesting to see how much is equivalent to that one fact, but I also can’t help but feel that some of the proofs could benefit from a different perspective.
Lohic less polished and less motivated, and more likely to just dump anv proof on you.
G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
It was recommended to me by Luke along with a number of other books as a potential way to learn provability logic. As before, the chapter provides actual examples for how to encode Turing machines as logical theories. Laurie Wilkes rated it liked it Mar 12, John Burgess has a list of corrections on his website, but it is better just to buy the corrected fifth edition.
If any of the below sounds surprising to you, you’d be well served by reading this chapter:. Simple, yet complete, presentation of the underlying theories of Computability; beautifully explained. This chapter would have been valuable before I started reading Model Theory. Eric Casteleijn rated it liked it Jun 27, Lewis Cawthorne rated it liked it Jun 28, This chapter shows how any recursive function can be expressed as a formula in the language of arithmetic a theory of first-order logic.
Jeffrey Ketland – – Analysis 66 4: This is another interesting exploration of the boundaries of undecidability. The chapter then discusses formal systems of arithmetic.
If you’re casually interested in math or computer science or if you need a brush up, or you just want a good time then I highly recommend reading this book at least through chapter 8. They’re a great way to brush up on your understanding of incompleteness, if you think you have to.
It walks you through the implementation of a Turing machine, and shows you a number of clever algorithms by which a Turing machine computes simple algorithms. Kogic if you’re already familiar with the result, reading this chapter is quite a bit of fun.
Computability and Logic by George S. Boolos
Read the ones that seem interesting, but don’t be afraid to skip the ones that seem boring. This chapter introduces provability logic and is the reason I picked up this textbook, initially.
This smoothly unifies diagonalization with the intuitive impossibility of the halting problem.