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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Book Review: Computability and Logic
Find it on Scholar. Adam Gardner rated it really liked it Dec 21, This book wasn’t the most useful book I’ve read in this series. I think this would be a great way to get people familiar with the type of logic problems they’ll have to be comfortable with if they’re going to tackle the rest of the course list and eventually MIRI research. Marcin Tkaczyk – – Roczniki Filozoficzne: Even if you’re vaguely familiar with the concept, but you’re not quite sure how a Turing machine works “wait, it only computabiliity a fixed number of states?
G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
This chapter left me a bit unsatisfied. Lewis Cawthorne rated it liked it Jun compufability, I can’t do it justice in a few mere paragraphs: Sheeru rated it liked it Mar 15, Boolos George and Jeffrey Richard.
As a minor note, this textbook had way more typos than any other textbook I’ve read. In any case, though, it’s good for the novice and even a worthwhile quick read for a more advanced audience who hasn’t seen this exact presentation before.
It’s a pretty solid introduction, and a good way to brush up on the precise syntax if you’re feeling rusty. Also, note that semirecursive sets are more commonly known as “recursively enumerable” sets. If you’re interested in model theory, this is a great place to get a feel for the ideas. It is a solid introduction to the concepts. These four functions are called the “primitive recursive” functions, and some time is spent exploring what they can do. Assumming little background knowledge, it has been incredibly satisfying to be shown how various computational systems work, and then also to show that they’re equivalent.
The second chapter of Computability and Logic is a clever and easy introduction to diagonalization, and I highly recommend it to newcomers. These are a set of building blocks for some pretty interesting functions, and we are now firmly in math land. It turns out that “monadic” logic first order logic in a language logic with only one-place relation symbols is decidable.
It actually shows you an encoding. Generally speaking, we can define sets and relations by indicator functions which distinguish between elements that are in a set from elements that are not. That said, it’s not a good introduction to modal provability logic.
Skordev, Computability in Combinatory Spaces. You’ll find yourself actually walking through the actions of the machine in your head, which is a great way to get a feel for the idealized basics of computation. If you’ve never played with nonstandard models before, this chapter is a nice introduction. bools
Chapter 18 anv particular is quite relevant to some of MIRI’s recent work, and is good to know in the LessWrong circles. PA is mentioned, but a more minimal and easier to reason about arithmetic is the focus of conversation.
Computability and Logic
This coputability was surprising, and the proof is a fun one. Eric Casteleijn rated it liked it Jun 27, Alternatively, you can resolve to deal only with sentences where all the quantifiers come first. We now move to the “further topics” section of the book. This chapter introduces enumerability, and some of the cooler results.
It was especially bad in the “Further Topics” section ch. I was somewhat disappointed with it: You get to play with sentences that describe a specific Turing machine and the state of its tape. I’m reviewing the books on the MIRI course list.
Will rated it really liked it Sep 18, Goodreads helps you keep track of books you want to read. Note that the indicator function for recursive sets must be total — i.
Computability and Logic by George S. Boolos
It demonstrates many difficult concepts with ease. It’s very interesting to see how much is equivalent to that one computabilitu, but I also can’t help but feel that some of the proofs could benefit from a different perspective. Bookhead rated it really liked it May 18,