Theoretical Computer Science
Logic programming in a fragment of intuitionistic linear logic
Papers presented at the IEEE symposium on Logic in computer science
Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Information and Computation
Contributions to the Theory of Logic Programming
Journal of the ACM (JACM)
Cut-elimination for a logic with definitions and induction
Theoretical Computer Science - Special issue on proof-search in type-theoretic languages
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
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
A logical framework for reasoning about logical specifications
A logical framework for reasoning about logical specifications
Model checking for π-calculus using proof search
CONCUR 2005 - Concurrency Theory
On the specification of sequent systems
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
From proofs to focused proofs: a modular proof of focalization in linear logic
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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
The Abella Interactive Theorem Prover (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
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
On the Expressivity of Minimal Generic Quantification
Electronic Notes in Theoretical Computer Science (ENTCS)
Least and Greatest Fixpoints in Game Semantics
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Algorithmic specifications in linear logic with subexponentials
PPDP '09 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming
Proof search specifications of bisimulation and modal logics for the π-calculus
ACM Transactions on Computational Logic (TOCL)
On the Proof Theory of Regular Fixed Points
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Finding unity in computational logic
Proceedings of the 2010 ACM-BCS Visions of Computer Science Conference
Fo(fd): Extending classical logic with rule-based fixpoint definitions
Theory and Practice of Logic Programming
Reasoning about computations using two-levels of logic
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Least and Greatest Fixed Points in Linear Logic
ACM Transactions on Computational Logic (TOCL)
Focused inductive theorem proving
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the addition of the exponentials (! and ?), we add least and greatest fixed point operators. The resulting logic, which we call µMALL=, satisfies two fundamental proof theoretic properties. In particular, µMALL= satisfies cut-elimination, which implies consistency, and has a complete focused proof system. This second result about focused proofs provides a strong normal form for cut-free proof structures that can be used, for example, to help automate proof search. We then consider applying these two results about µMALL= to derive a focused proof system for an intuitionistic logic extended with induction and co-induction. The traditional approach to encoding intuitionistic logic into linear logic relies heavily on using the exponentials, which unfortunately weaken the focusing discipline. We get a better focused proof system by observing that certain fixed points satisfy the structural rules of weakening and contraction (without using exponentials). The resulting focused proof system for intuitionistic logic is closely related to the one implemented in Bedwyr, a recent model checker based on logic programming. We discuss how our proof theory might be used to build a computational system that can partially automate induction and co-induction.