Proofs and types
Handbook of logic in computer science (vol. 2)
Basic proof theory
Operational Logic of Proofs with Functionality Condition on Proof Predicate
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Justification logic and history based computation
ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
Strong normalization and confluence for reflexive combinatory logic
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
A modal logic internalizing normal proofs
Information and Computation
Reflections on trust: trust assurance by dynamic discovery of static properties
FAST'09 Proceedings of the 6th international conference on Formal Aspects in Security and Trust
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We introduce a general purpose typed 驴-calculus 驴 驴 which contains intuitionistic logic, is capable of internalizing its own derivations as 驴-terms and yet enjoys strong normalization with respect to a natural reduction system. In particular, 驴驴 subsumes the typed 驴-calculus. The Curry-Howard isomorphism converting intuitionistic proofs into 驴-terms is a simple instance of the internalization property of 驴驴. The standard semantics of 驴驴 is given by a proof system with proof checking capacities. The system 驴驴 is a theoretical prototype of reflective extensions of a broad class of type-based systems in programming languages, provers, AI and knowledge representation, etc.