Theoretical Computer Science
Linear objects: logical processes with built-in inheritance
Logic programming
Proceedings of the workshop on Advances in linear logic
Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Information and Computation
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
The Structure of Exponentials: Uncovering the Dynamics of Linear Logic Proofs
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Concurrent Games and Full Completeness
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
Soft linear logic and polynomial time
Theoretical Computer Science - Implicit computational complexity
LJQ: a strongly focused calculus for intuitionistic logic
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Testing concurrent systems: an interpretation of intuitionistic logic
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Focusing and polarization in intuitionistic logic
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Focusing Strategies in the Sequent Calculus of Synthetic Connectives
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Types for Proofs and Programs
Algorithmic specifications in linear logic with subexponentials
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Focusing and polarization in linear, intuitionistic, and classical logics
Theoretical Computer Science
Least and greatest fixed points in linear logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
From Focalization of Logic to the Logic of Focalization
Electronic Notes in Theoretical Computer Science (ENTCS)
Magically constraining the inverse method using dynamic polarity assignment
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
On the meaning of focalization
Ludics, dialogue and interaction
Least and Greatest Fixed Points in Linear Logic
ACM Transactions on Computational Logic (TOCL)
Compact proof certificates for linear logic
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
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Probably the most significant result concerning cut-free sequent calculus proofs in linear logic is the completeness of focused proofs. This completeness theorem has a number of proof theoretic applications -- e.g. in game semantics, Ludics, and proof search -- and more computer science applications -- e.g. logic programming, call-by-name/value evaluation. Andreoli proved this theorem for first-order linear logic 15 years ago. In the present paper, we give a new proof of the completeness of focused proofs in terms of proof transformation. The proof of this theorem is simple and modular: it is first proved for MALL and then is extended to full linear logic. Given its modular structure, we show how the proof can be extended to larger systems, such as logics with induction. Our analysis of focused proofs will employ a proof transformation method that leads us to study how focusing and cut elimination interact. A key component of our proof is the construction of a focalization graph which provides an abstraction over how focusing can be organized within a given cut-free proof. Using this graph abstraction allows us to provide a detailed study of atomic bias assignment in a way more refined that is given in Andreoli's original proof. Permitting more flexible assignment of bias will allow this completeness theorem to help establish the completeness of a number of other automated deduction procedures. Focalization graphs can be used to justify the introduction of an inference rule for multifocus derivation: a rule that should help us better understand the relations between sequentiality and concurrency in linear logic.