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Linear Logic as a Good Logical Foundation for Computer Science - A brief analysis of the computational aspects of linear logic by Max Kanovich.
A New Deconstructive Logic: Linear Logic (1997) - Article by V. Danos, J.-B. Joinet and H. Schellinx outlining how linear logic can function as a `mark-up logic' allowing the embedding of a large class of logics in a manner that respects their underlying proof semantics (cf. Nuel Belnap's Display Logic).
On the Formulae-as-Types Correspondence for Classical Logic - Doctoral thesis of Charles Stewart, which investigates foundational aspects of the application of the formulae-as-types correspondence to classical logic, and extends the treatment to include intensional equality and induction.
A Curry-Howard Foundation for Functional Computation with Control (1997) - Article by C.-H. L. Ong and C. A. Stewart which presents a call-by-name variant of Parigot's lambda-mu calculus. The calculus is proposed as a foundation for first-class continuations and statically scoped exceptions in functional programming languages.
Game Semantics or Linear Logic? - A discussion of how linear logic relates to computability logic - the game-sematically introduced logic of computational resources and interactive computation.
Phil Wadler's Linear Logic Publications - Includes his tutorial paper "A taste of linear logic".
Logic Programming in the LF Logical Framework (1991) - Article by Frank Pfennig describing a logic programming language which serves as a proof search engine for LF.
Computational Isomorphisms in Classical Logic - Article by V. Danos, J. B. Joinet and H. Schellinx examining the categorical semantics of classical logic from a persepctive inspired by linear logic.
Interpretability Logic - Open Encyclopedia article.
Provability Logic - Open Encyclopedia article.

Wikipedia Articles

New Foundations - In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name.
Foundations of mathematics - Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathematics is also a central question of the philosophy of mathematics: On what ultimate basis can mathematical statements be called true?
James Earl Baumgartner - James Earl Baumgartner is an American mathematician active in set theory, mathematical logic and foundations, and topology. He is an emeritus professor at Dartmouth College.
Kaina Stoicheia - Kaina Stoicheia (Καινα στοιχεια) or "New Elements" is the title of several manuscript drafts of a document that Charles Sanders Peirce wrote circa 1904, intended as a preface to a book on the foundations of mathematics. It presents a consummate integration of his ideas on the interrelations of logic, mathematics, and semeiotic, or the theory of signs.
Frege's theorem - Frege's theorem states that the (Peano) axioms of arithmetic can be derived in second-order logic from Hume's principle. It was first proven, informally, by Gottlob Frege in his Die Grundlagen der Arithmetik (Foundations of Arithmetic), published in 1884, and proven more formally in his Grundgesetze der Arithmetik (Basic Laws of Arithmetic), published in two volumes, in 1893 and 1903.