Theoretical Computer Science
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
From proof-nets to interaction nets
Proceedings of the workshop on Advances in linear logic
The undecidability of second order multiplicative linear logic
Information and Computation
Phase semantic cut-elimination and normalization proofs of first- and higher-order linear logic
Theoretical Computer Science - Special issue on linear logic, 1
Categorical Reconstruction of a Reduction Free Normalization Proof
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Phase semantics for light linear logic
Theoretical Computer Science - Linear logic
Normalization by Evaluation for Typed Lambda Calculus with Coproducts
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Phase semantics for light linear logic
Theoretical Computer Science - Linear logic
Phase semantics and decidability of elementary affine logic
Theoretical Computer Science - Logic, semantics and theory of programming
Intuitionistic phase semantics is almost classical
Mathematical Structures in Computer Science
On the Convergence of Reduction-based and Model-based Methods in Proof Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
A Constructive Semantic Approach to Cut Elimination in Type Theories with Axioms
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Forcing-Based Cut-Elimination for Gentzen-Style Intuitionistic Sequent Calculus
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Journal of Logic, Language and Information
A simple proof that super-consistency implies cut elimination
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Truth values algebras and proof normalization
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Orthogonality and Boolean algebras for deduction modulo
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Polarized classical non-associative Lambek calculus and formal semantics
LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics
Semantic cut elimination in the intuitionistic sequent calculus
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Polarized montagovian semantics for the Lambek-Grishin calculus
FG'10/FG'11 Proceedings of the 15th and 16th international conference on Formal Grammar
Remarks on semantic completeness for proof-terms with Laird's dual affine/intuitionistic λ-Calculus
Rewriting Computation and Proof
Nondeterministic Phase Semantics and the Undecidability of Boolean BI
ACM Transactions on Computational Logic (TOCL)
Strong Normalization in the π-calculus with Intersection and Union Types
Fundamenta Informaticae - Intersection Types and Related Systems ITRS
Reasoning about Resources and Information: A Linear Logic Approach
Fundamenta Informaticae
| Hi-index | 5.23 |
We present a natural generalization of Girard's (first order) phase semantics of linear logic (Theoret. Comput. Sci. 50 (1987)) to intuitionistic and higher-order phase semantics. Then we show that this semantic framework allows us to derive a uniform semantic proof of the (first order and) higher order cut-elimination theorem (as well as a (first order and) higher order phase-semantic completeness theorem) for various different logical systems at the same time. Our semantic proof works for various different logical systems uniformly in a strong sense (without any change of the argument of proof): it works for both first order and higher order versions and for linear, substructural, and standard logics uniformly, and for both their intuitionistic and classical versions uniformly.