Could someone recommend me a logic textbook? I need it to cover syntax and semantics for propositional and first-order classical logic, as well as preferably including material on intuitionistic logic and higher-order logics. I could really use material on any existing attempts to ground semantics or proof systems in computation, too.
“Computation and Logic” is my first candidate, though I want something else to go with it. This is for trying to work on logical probability research, and also because I’ve always been interested in type theory as a research field (hence wanting coverage of intuitionistic logic, which might as well be called computational logic what with the Curry-Howard Isomorphism).
The first five chapters of Marker’s Model Theory will satisfy
syntax and semantics for propositional and first-order classical logic
and some information about type theory in the context of model theory. I know it doesn’t satisfy all of your requirements, but it is a seriously good book with an excellent learning curve. I took a semester course covering the first three chapters in undergrad. It almost convinced me to work in mathematical logic, but sadly economic incentives trumped aesthetic ones.
This is the textbook we used in graduate school, and it is very good. Not sure if this is what you were referring to as “Computation and Logic”. It covers second order logic, but not intuitionistic logic as far as I can remember.
Could someone recommend me a logic textbook? I need it to cover syntax and semantics for propositional and first-order classical logic, as well as preferably including material on intuitionistic logic and higher-order logics. I could really use material on any existing attempts to ground semantics or proof systems in computation, too.
“Computation and Logic” is my first candidate, though I want something else to go with it. This is for trying to work on logical probability research, and also because I’ve always been interested in type theory as a research field (hence wanting coverage of intuitionistic logic, which might as well be called computational logic what with the Curry-Howard Isomorphism).
The first five chapters of Marker’s Model Theory will satisfy
and some information about type theory in the context of model theory. I know it doesn’t satisfy all of your requirements, but it is a seriously good book with an excellent learning curve. I took a semester course covering the first three chapters in undergrad. It almost convinced me to work in mathematical logic, but sadly economic incentives trumped aesthetic ones.
This is the textbook we used in graduate school, and it is very good. Not sure if this is what you were referring to as “Computation and Logic”. It covers second order logic, but not intuitionistic logic as far as I can remember.
That’s indeed the one I was referring to.