Sequent Calculus and the Speciication of Computation Lecture Notes

Sequent Calculus and the Speciication of Computation Lecture Notes

Lecture Notes on Classical Linear Logic

Originally, linear logic was conceived by Girard [Gir87] as a classical system, with one-sided sequents, an involutive negation, and an appropriate law of excluded middle. For a number of the applications, such as functional computation, logic programming, and implicit computational complexity the intuitionistic version is more suitable. In the case of concurrent computation, both classical and...

Sequent Calculus and the Specification of Computation Lecture Notes

The sequent calculus has been used for many purposes in recent years within theoretical computer science. In these lectures, we shall highlight some of its uses in the specification of and reasoning about computation. During the search for cut-free sequent proofs, the formulas in sequents are re-arranged and replaced with other formulas. Such changes can be used to model the dynamics of computa...

Maude as a Platform for Designing and Implementing Deep Inference Systems

Deep inference is a proof theoretical methodology that generalizes the traditional notion of inference in the sequent calculus: in contrast to the sequent calculus, the deductive systems with deep inference do not rely on the notion of main connective, and permit the application of the inference rules at any depth inside logical expressions, in a way which resembles the application of term rewr...

Towards a Duration Calculus Proof Assistant in PVS

The Duration Calculus (DC) is an interval temporal logic for reasoning about real-time systems. This paper describes a tool for constructing DC speciications and checking DC proofs. The proof assistant is implemented by encoding the semantics of DC within the higher-order logic of a general-purpose speciication and veriication environment called PVS. We develop a Gentzen style sequent proof sys...