Handbook of logic in computer science (vol. 2)
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Theorem Proving via General Matings
Journal of the ACM (JACM)
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
System Description: Teyjus - A Compiler and Abstract Machine Based Implementation of lambda-Prolog
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Journal of Automated Reasoning
Polymorphic lemmas and definitions in $\lambda$Prolog and Twelf
Theory and Practice of Logic Programming
Trust and Automation in Verification Tools
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Focusing and polarization in linear, intuitionistic, and classical logics
Theoretical Computer Science
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
Incorporating tables into proofs
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Compact proof certificates for linear logic
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Foundational proof certificates: making proof universal and permanent
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Foundational proof certificates in first-order logic
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Recent developments in the theory of focused proof systems provide flexible means for structuring proofs within the sequent calculus. This structuring is organized around the construction of “macro” level inference rules based on the “micro” inference rules which introduce single logical connectives. After presenting focused proof systems for first-order classical logics (one with and one without fixed points and equality) we illustrate several examples of proof certificates formats that are derived naturally from the structure of such focused proof systems. In principle, a proof certificate contains two parts: the first part describes how macro rules are defined in terms of micro rules and the second part describes a particular proof object using the macro rules. The first part, which is based on the vocabulary of focused proof systems, describes a collection of macro rules that can be used to directly present the structure of proof evidence captured by a particular class of computational logic systems. While such proof certificates can capture a wide variety of proof structures, a proof checker can remain simple since it must only understand the micro-rules and the discipline of focusing. Since proofs and proof certificates are often likely to be large, there must be some flexibility in allowing proof certificates to elide subproofs: as a result, proof checkers will necessarily be required to perform (bounded) proof search in order to reconstruct missing subproofs. Thus, proof checkers will need to do unification and restricted backtracking search.