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Commentary by Chris Pressey

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Logic

Logic (Hodges)

A very gentle, informal, conversational introduction to elementary logic.

Mathematical logic and formalized theories

A fairly gentle introduction to formal logic, starting with propositional logic, then first-order, first-order with equality, second-order logic, then the Peano axioms, and so on.

Mathematical Logic (Kleene)

A book on mathematical logic written by Kleene.

Mathematical Logic (Quine)

A book on mathematical logic written by Quine.

Deductive Logic: a programed introduction

"Programed" means the thing is one big exercise sheet. Individual questions with answers are called "frames". In fact, "The Little Lisper", "The Little Schemer", "The Reasoned Schemer", etc, are all in this format too.

The Blackwell Guide To Philosophical Logic

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Handbook of Logic in Computer Science, Volume 1

1. (Valuation Systems and Consequence Relations)

2. (Recursion Theory)

3. Universal Algebra

Section 2.3 -- algebraic semantics of WHILE programs

Section 3.3 -- congruences and quotient algebras

5. (Category Theory)

6. Topology

some interesting connections to liveness etc but maybe not all that great

Section 3.4 closure operators

7. (Model Theory)

Handbook of Logic and Proof Techniques for Computer Science

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Handbook of logic in artificial intelligence and logic programming, Vol 1

Notes on Chapter "Equational Reasoning and Term Rewriting Systems" by David A. Plaisted, pp. 273:

It has the rules of inference for equational logic in it, but comes at it from a slightly different angle: an equation is a pair of terms with = in the middle, and a set of equations is an "equation system"; and any equation system can be manipulated using These 5 Weird Rules.

Goes into term rewriting, with the usual stuff: confluence, critical pairs, Knuth-Bendix completion...

Simply Logical

Intro to logic using Prolog. Keeps calling it "clausal logic", which is probably a good thing, in this context. The use of logic programming to teach logic is interesting, and there is a fully interactive online version where you can execute the examples and play with them to understand them better, which is almost certainly also a good thing, but the jury's still out, as far as I'm concerned, on whether it results in a good way to learn logic; I have a hard time seeing how this book is not "just" teaching logic programming "instead".

Introduction to Mathematical Proof

Basically a short (91 pages) introductory textbook on the subject of applying logic to mathematical reasoning for undergraduates to start writing proofs.

It's open source and it discusses a number of toy proof systems, and these two things alone probably place it above a considerable number of other tutorials.

On the Unusual Effectiveness of Logic in Computer Science

The basic idea is that logic informs computer science, a lot. The examples they give are

This is not, btw, the one with "Blackboard Scheme". I think I know which one that was, but it's not this one.

The Galois Connection between Syntax and Semantics

Smith goes into how there is a Galois connection between the syntax and semantics of a logical system. I think the idea could be applied to any formal language that has been given a semantics. (Is semantics a quotient of syntax? Does taking a quotient induce a Galois connection? I wonder, I mean, I think so because it seems to just be two different ways of talking about the same thing, or at least closely related things...)

Syntax versus Semantics

Distinguishing symbols pertaining to the syntax, from symbols pertaining to the semantics, by colouring them differently.

Towards Applied Theories based on Computability Logic

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Propositional Logic \| Internet Encyclopedia of Philosophy

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Natural Deduction \| Internet Encyclopedia of Philosophy

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Natural Deduction Systems in Logic (Stanford Encyclopedia of Philosophy)

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Second-order and Higher-order Logic (Stanford Encyclopedia of Philosophy)

future-rating: 2.5

Survey of Computability Logic

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Provability Logic (Stanford Encyclopedia of Philosophy)

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Intensional Logic (Stanford Encyclopedia of Philosophy)

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The Herbrand Manifesto

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Self-verifying theories - Wikipedia

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Bernays--Schönfinkel class - Wikipedia

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Are opinions considered sentences in logic? - Philosophy Stack Exchange

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lo.logic - Metamathematics of buts - MathOverflow

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logic - What framework or tool solves the Barber Paradox? - Philosophy Stack Exchange

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What assumptions and methodology do metaproofs of logic theorems use and employ? - MathOverflow

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