The polynomial hierarchy and intuitionistic bounded arithmetic
Proc. of the conference on Structure in complexity theory
The monotone circuit complexity of Boolean functions
Combinatorica
General theory of cumulative inference
Proceedings of the 2nd international workshop on Non-monotonic reasoning
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
Exponential lower bounds for the pigeonhole principle
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
Exponential lower bounds for the pigeonhole principle
Computational Complexity
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An exponential lower bound to the size of bounded depth Frege proofs of the Pigeonhole Principle
Random Structures & Algorithms
Some consequences of cryptographical conjectures for S12 and EF
Information and Computation - Special issue: logic and computational complexity
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Lower bounds for the polynomial calculus
Computational Complexity
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Proof-complexity results for nonmonotonic reasoning
ACM Transactions on Computational Logic (TOCL)
Modal logic
Sequent calculi for propositional nonmonotonic logics
ACM Transactions on Computational Logic (TOCL)
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
From Abstract Data Types to Logical Frameworks
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
Nonmonotonic reasoning: towards efficient calculi and implementations
Handbook of automated reasoning
On the lengths of proofs in the propositional calculus.
On the lengths of proofs in the propositional calculus.
Mathematical modal logic: a view of its evolution
Journal of Applied Logic
Pseudorandom Generators in Propositional Proof Complexity
SIAM Journal on Computing
Interpolation and Definability in Modal Logics (Oxford Logic Guides)
Interpolation and Definability in Modal Logics (Oxford Logic Guides)
On the complexity of the disjunction property in intuitionistic and modal logics
ACM Transactions on Computational Logic (TOCL)
Admissible Rules of Modal Logics
Journal of Logic and Computation
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity
Admissible Rules of Łukasiewicz Logic
Journal of Logic and Computation
Bases of Admissible Rules of Łukasiewicz Logic
Journal of Logic and Computation
Proof complexity of propositional default logic
Archive for Mathematical Logic
Proof complexity of non-classical logics
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
The complexity of theorem proving in autoepistemic logic
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
Proof complexity is an interdisciplinary area of research utilising techniques from logic, complexity, and combinatorics towards the main aim of understanding the complexity of theorem proving procedures. Traditionally, propositional proofs have been the main object of investigation in proof complexity. Due their richer expressivity and numerous applications within computer science, also non-classical logics have been intensively studied from a proof complexity perspective in the last decade, and a number of impressive results have been obtained. In these notes we give an introduction to this recent field of proof complexity of non-classical logics. We cover results from proof complexity of modal, intuitionistic, and non-monotonic logics. Some of the results are surveyed, but in addition we provide full details of a recent exponential lower bound for modal logics due to Hrubeš [60] and explain the complexity of several sequent calculi for default logic [16,13]. To make the text self-contained, we also include necessary background information on classical proof systems and non-classical logics.