Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Automated deduction by theory resolution
Journal of Automated Reasoning
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Proof methods for equational theories
Proof methods for equational theories
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Proofs and types
Journal of Symbolic Computation
A resolution principle for clauses with constraints
CADE-10 Proceedings of the tenth international conference on Automated deduction
Term rewriting: Some experimental results
Journal of Symbolic Computation
Handbook of theoretical computer science (vol. B)
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Use of replace rules in theorem proving
Methods of Logic in Computer Science
Information and Computation
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
Term rewriting and all that
Orderings automated theorem proving
MAAI '96 Proceedings of symposia in applied mathematics on Mathematical aspects of artificial intelligence
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Higher order unification via explicit substitutions
Information and Computation
Solution of the Robbins Problem
Journal of Automated Reasoning
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
Equational rules for rewriting logic
Theoretical Computer Science - Rewriting logic and its applications
Lambda-calculus, Combinators and the Comprehension Scheme
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Proof Normalization for a First-Order Formulation of Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Axioms vs. Rewrite Rules: From Completeness to Cut Elimination
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Higher-Order Equational Unification via Explicit Substitutions
ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
Positive Deduction modulo Regular Theories
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
AC-Superposition with Constraints: No AC-Unifiers Needed
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
A Model-Based Completeness Proof of Extended Narrowing and Resolution
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Constrained resolution: a complete method for higher-order logic.
Constrained resolution: a complete method for higher-order logic.
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
External Rewriting for Skeptical Proof Assistants
Journal of Automated Reasoning
ELAN from a rewriting logic point of view
Theoretical Computer Science - Rewriting logic and its applications
Binding Logic: Proofs and Models
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Termination of rewriting in the Calculus of Constructions
Journal of Functional Programming
Formal validation of pattern matching code
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Abstract canonical presentations
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Eigenvariables, bracketing and the decidability of positive minimal predicate logic
Theoretical Computer Science
Semantic foundations for generalized rewrite theories
Theoretical Computer Science
A Framework for Defining Logical Frameworks
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Convergence of Reduction-based and Model-based Methods in Proof Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
Strong normalisation in two pure pattern type systems
Mathematical Structures in Computer Science
Cut Elimination in Deduction Modulo by Abstract Completion
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
A Constructive Semantic Approach to Cut Elimination in Type Theories with Axioms
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
A Conditional Logical Framework
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Types for Proofs and Programs
Integration Testing from Structured First-Order Specifications via Deduction Modulo
ICTAC '09 Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing
Annals of Mathematics and Artificial Intelligence
Detecting Inconsistencies in the Gene Ontology Using Ontology Databases with Not-gadgets
OTM '09 Proceedings of the Confederated International Conferences, CoopIS, DOA, IS, and ODBASE 2009 on On the Move to Meaningful Internet Systems: Part II
Journal of Automated Reasoning
The stratified foundations as a theory modulo
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Confluence as a cut elimination property
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Embedding pure type systems in the lambda-pi-calculus modulo
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
A simple proof that super-consistency implies cut elimination
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Algorithmic equality in Heyting arithmetic modulo
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
On constructive cut admissibility in deduction modulo
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Truth values algebras and proof normalization
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
A finite first-order theory of classes
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Theorem proving modulo based on Boolean equational procedures
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Automating theories in intuitionistic logic
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
All about maude - a high-performance logical framework: how to specify, program and verify systems in rewriting logic
On the confluence of lambda-calculus with conditional rewriting
Theoretical Computer Science
Embedding deduction modulo into a prover
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
A sequent calculus with implicit term representation
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
A simple class of Kripke-style models in which logic and computation have equal standing
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Orthogonality and Boolean algebras for deduction modulo
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Experimenting with deduction modulo
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
A semantic completeness proof for tamed
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
On the confluence of λ-calculus with conditional rewriting
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
TLDI '12 Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation
Rule-based programming and proving: the ELAN experience outcomes
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
What do we know when we know that a theory is consistent?
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Semantic cut elimination in the intuitionistic sequent calculus
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
A proposal for broad spectrum proof certificates
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Combining Deduction Modulo and Logics of Fixed-Point Definitions
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
A theory independent curry-de bruijn-howard correspondence
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
LFP: a logical framework with external predicates
Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Rewriting Computation and Proof
Rewriting Computation and Proof
Unbounded proof-length speed-up in deduction modulo
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of general interest because it permits one to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo that gives a proof-theoretic account of the combination of computations and deductions. The congruence on propositions is handled through rewrite rules and equational axioms. Rewrite rules apply to terms but also directly to atomic propositions.The second contribution is to give a complete proof search method, called extended narrowing and resolution (ENAR), for theorem proving modulo such congruences. The completeness of this method is proved with respect to provability in sequent calculus modulo.An important application is that higher-order logic can be presented as a theory in deduction modulo. Applying the ENAR method to this presentation of higher-order logic subsumes full higher-order resolution.