Niveau: Supérieur
A formal framework for specifying sequent calculus proof systems Dale Millera, Elaine Pimentelb aINRIA Saclay and LIX/Ecole Polytechnique, 91128 Palaiseau, France bDepartamento de Matematicas, Universidad del Valle, Cali, Colombia and Departamento de Matematica, UFMG, Belo Horizonte, Brazil Abstract Intuitionistic logic and intuitionistic type systems are commonly used as frame- works for the specification of natural deduction proof systems. In this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequences of encoded sequent calculus proof systems. In particular, derivability of an inference rule from a set of inference rules can be decided by bounded (linear) logic program- ming search on the encoded rules. We also present two simple and decidable conditions that guarantee that the cut rule and non-atomic initial rules can be eliminated. Keywords: logical frameworks, linear logic, sequent calculus, proof systems, cut elimination 1. Introduction Intuitionistic logic with quantification at (non-predicate) higher-order types [1, 2, 3] and dependently typed ?-calculi [4, 5, 6] can be used as meta-logics to specify proof systems for a range of object logics. A major advantage of using a “logical” or “type-theoretical” framework to specify a proof system is that they support levels of abstraction that facilitate writing declarative specifications of object-logic proof systems.
- inference rules
- rules can
- linear logic
- initial rule duality
- big-step rule
- can provide partial
- intuitionistic logic
- proof systems
- sequent calculus