Automated Deduction - CADE 28 28th International Conference on Automated Deduction, Virtual Event, July 12-15, 2021, Proceedings
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is...
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| Médium: | E-kniha |
| Jazyk: | English |
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Netherlands
Springer Nature
2021
Springer International Publishing AG |
| Vydanie: | 1 |
| Edícia: | Lecture Notes in Computer Science; Lecture Notes in Artificial Intelligence |
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| ISBN: | 3030798763, 9783030798765, 3030798755, 9783030798758 |
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| Abstract | This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions. |
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| AbstractList | This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions. |
| Author | Sutcliffe, Geoff Platzer, André |
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| Snippet | This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full... |
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| SubjectTerms | Artificial intelligence automata theory boolean functions Computer architecture & logic design computer programming Computer programming / software engineering Computer science Computer Science Logic and Foundations of Programming Computing and Information Technology first order logic formal languages Formal Languages and Automata Theory formal logic logic programming Logics and Meanings of Programs Mathematical Logic and Formal Languages Mathematical theory of computation model checking program verification semantics software architecture software design Software Engineering software quality software verification Special computer methods theorem provers theorem proving |
| Subtitle | 28th International Conference on Automated Deduction, Virtual Event, July 12-15, 2021, Proceedings |
| TableOfContents | Intro -- Preface -- Organization -- Contents -- Invited Talks -- Non-well-founded Deduction for Induction and Coinduction -- 1 Introduction -- 2 The Principles of Induction and Coinduction -- 2.1 Algebraic Formalization of Induction and Coinduction -- 2.2 Transitive (Co)closure Operators -- 3 Non-well-founded Deduction for Induction -- 3.1 Non-well-founded Proof Theory -- 3.2 Explicit vs. Implicit Induction in Transitive Closure Logic -- 4 Adding Coinductive Reasoning -- 4.1 Implicit Coinduction in Transitive (Co)closure Logic -- 4.2 Applications in Automated Proof Search -- 4.2.1 Program Equivalence in the TcC Framework -- 5 Perspectives and Open Questions -- 5.1 Implementing Non-well-founded Machinery -- 5.2 Relative Power of Explicit and Implicit Reasoning -- References -- Towards the Automatic Mathematician -- 1 Introduction -- 2 Towards the Automatic Mathematician -- 2.1 Neural Network Architectures -- 2.2 Training Methodology -- 2.3 Instant Utilization of New Premises -- 2.4 Natural Language -- 3 Conclusion -- References -- Logical Foundations -- Tableau-based Decision Procedure for Non-Fregean Logic of Sentential Identity -- 1 Introduction -- 2 SCI -- 3 Tableaux -- 3.1 Tableau System for SCI -- 3.2 Soundness and Completeness4 -- 3.3 Termination -- 3.4 Limiting the Number of Labels -- 4 Implementation -- 4.1 Overview -- 4.2 Technical Notes -- 4.3 Test Results -- 5 Conclusions -- References -- Learning from Łukasiewicz and Meredith: Investigations into Proof Structures -- 1 Introduction -- 2 Relating Formal Human Proofs with ATP Proofs -- 3 Condensed Detachment and a Formal Basis -- 3.1 Proof Structures: D-Terms, Tree Size and Compacted Size -- 3.2 Proof Structures, Formula Substitutions and Semantics -- 4 Reducing the Proof Size by Replacing Subproofs -- 5 Properties of Meredith's Refined Proof -- 6 First Experiments -- 7 Conclusion References -- Superposition with First-class Booleans and Inprocessing Clausification -- 1 Introduction -- 2 Logic -- 3 The Calculus -- 4 Refutational Completeness -- 5 Inprocessing Clausification Methods -- 6 Implementation -- 7 Evaluation -- 8 Related Work and Conclusion -- Acknowledgment -- References -- Superposition for Full Higher-order Logic -- 1 Introduction -- 2 Logic -- 3 The Calculus -- 4 Refutational Completeness -- 5 Implementation -- 6 Evaluation -- 7 Conclusion -- Acknowledgment -- References -- Implementation and Application -- Making Higher-Order Superposition Work -- 1 Introduction -- 2 Background and Setting -- 3 Preprocessing Higher-Order Problems -- 4 Reasoning about Formulas -- 5 Enumerating Infinitely Branching Inferences -- 6 Controlling Prolific Rules -- 7 Controlling the Use of Backends -- 8 Comparison with Other Provers -- 9 Discussion and Conclusion -- References -- Dual Proof Generation for Quantified Boolean Formulas with a BDD-based Solver -- 1 Introduction -- 2 Background Preliminaries -- 3 Logical Foundations -- 3.1 Inference Rules -- 3.2 Integrating Proof Generation into BDD Operations -- 4 Integrating Proof Generation into a QBF Solver -- 4.1 Dual Proof Generation -- 4.2 Clause Removal -- 4.3 Specializing to Refutation or Satisfaction Proofs -- 5 Experimental Results -- 6 Conclusions -- Acknowledgements. -- References -- Reliable Reconstruction of Fine-grained Proofs in a Proof Assistant -- 1 Introduction -- 2 veriT and Proofs -- 3 Overview of the veriT-Powered smt Tactic -- 4 Tuning the Reconstruction -- 4.1 Preprocessing Rules -- 4.2 Implicit Steps -- 4.3 Arithmetic Reasoning -- 4.4 Selective Decoding of the First-order Encoding -- 4.5 Skipping Steps -- 5 Evaluation -- 5.1 Strategies -- 5.2 Improvements of Sledgehammer Results -- 5.3 Speed of Reconstruction -- 6 Related Work -- 7 Conclusion -- References References -- Efficient Local Reductions to Basic Modal Logic -- 1 Introduction -- 2 Preliminaries -- 3 Layered Normal Form with Sets of Levels -- 4 Correctness -- 5 Comparison With Related Work -- 6 Evaluation -- 7 Conclusion and Future Work -- References -- Isabelle's Metalogic: Formalization and Proof Checker -- 1 Introduction -- 2 Related Work -- 3 Preliminaries -- 4 Types and Terms -- 5 Classes and Sorts -- 6 Signatures -- 7 Logic -- 7.1 Basic Inference Rules -- 7.2 Equality -- 7.3 Type Class Reasoning -- 8 Proof Terms and Checker -- 9 Size and Structure of the Formalization -- 10 Integration with Isabelle -- 11 Running the Proof Checker -- 12 Trust Assumptions -- 13 Future Work -- A Appendix -- References -- Theory and Principles -- The ksmt Calculus Is a δ-complete Decision Procedure for Non-linear Constraints -- 1 Introduction -- 2 Preliminaries -- 3 The ksmt Calculus -- 3.1 Sufficient Termination Conditions -- 4 δ-decidability -- 5 δ-ksmt -- 5.1 Soundness -- 5.2 δ-completeness -- 6 Local ε-full Linearisations -- 7 Conclusion -- References -- Universal Invariant Checking of Parametric Systems with Quantifier-free SMT Reasoning -- 1 Introduction -- 2 Preliminaries -- 3 Modeling Parametric Systems as Array-based Transition Systems -- 3.1 Universal invariant problem for array-based systems -- 4 Overview of the Method -- 5 Modified Parameter Abstraction -- 5.1 Abstraction Computation -- 5.2 Stuttering Simulation -- 6 Refinement -- 6.1 From Invariants to Universal Lemmas -- 7 Related Work -- 8 Experimental Evaluation -- 9 Conclusions -- References -- Politeness and Stable Infiniteness: Stronger Together -- 1 Introduction -- 2 Preliminaries -- 2.1 Signatures and Structures -- 2.2 Polite Theories -- 3 Politeness and Strong Politeness -- 3.1 Witnesses vs. Strong Witnesses -- 3.2 A Polite Theory that is not Strongly Polite 3.3 The Case of Mono-sorted Polite Theories -- 3.4 Mono-sorted Finite Witnessability -- 4 A Blend of Polite and Stably-Infinite Theories -- 4.1 Refined Combination Theorem -- 4.2 Proof of Theorem 4 -- 5 Preliminary Case Study -- 6 Conclusion -- References -- Equational Theorem Proving Modulo -- 1 Introduction -- 2 Preliminaries -- 3 Constrained Clauses -- 4 Inference Rules -- 5 Redundancy Criteria and Contraction Techniques -- 6 Refutational Completeness -- 7 Conclusion -- References -- Unifying Decidable Entailments in Separation Logic with Inductive Definitions -- 1 Introduction -- 2 Definitions -- 3 Decidable Entailment Problems -- 4 Reducing Safe to Established Entailments -- 4.1 Expansions and Truncations -- 4.2 Transforming the Consequent -- 4.3 Transforming the Antecedent -- 4.4 Transforming Entailments -- 5 Conclusion and Future Work -- References -- Subformula Linking for Intuitionistic Logic with Application to Type Theory -- 1 Introduction -- 2 Subformula Linking for Intuitionistic First-Order Logic -- 2.1 The Propositional Fragment -- 2.2 Quantifiers -- 3 Incorporating Arity-Typed λ-Terms -- 4 Application: Embedding Intuitionistic Type Theories -- 5 Conclusion and Future Directions -- References -- Efficient SAT-based Proof Search in Intuitionistic Propositional Logic -- 1 Introduction -- 2 Preliminary Notions -- 3 The Calculus C→ -- 4 The Procedure proveR -- 5 Related Work and Experimental Results -- References -- Proof Search and Certificates for Evidential Transactions -- 1 Introduction -- 2 Cyberlogic Proof Theory -- 3 Cyberlogic Programs -- 3.1 Cyberlogic Program Syntax -- 3.2 CPS Proof Search -- 4 Proof Certificates -- 5 Related Work -- 6 Conclusions -- References -- Non-clausal Redundancy Properties -- 1 Introduction -- 2 Preliminaries -- 3 Redundancy for Boolean Functions -- 4 BDD Redundancy Properties An Automated Approach to the Collatz Conjecture 5 Gaussian Elimination -- 6 Results -- 7 Conclusion -- References -- Multi-Dimensional Interpretations for Termination of Term Rewriting -- 1 Introduction -- 2 Preliminaries -- 3 Notes on Reduction Pairs -- 4 Interpretation Methods as Derivers -- 5 Multi-Dimensional Interpretations -- 6 Arctic Interpretations -- 7 Strict Monotonicity -- 8 Implementation and Experiments -- 9 Conclusion -- References -- Finding Good Proofs for Description Logic Entailments using Recursive Quality Measures -- 1 Introduction -- 2 Preliminaries -- 2.1 Proofs -- 2.2 Derivers -- 3 Measuring Proofs -- 3.1 Monotone Recursive Measures -- 4 Complexity Results -- 4.1 The General Case -- 4.2 Proof Depth -- 4.3 The Tree Size Measure -- 5 Conclusion -- References -- Computing Optimal Repairs of Quantified ABoxes w.r.t. Static EL TBoxes -- 1 Introduction -- 2 Preliminaries -- 3 A Tale of Two Entailments -- 3.1 Classical Entailment and CQ-Entailment -- 3.2 IQ-Entailment -- 4 Canonical Repairs -- 5 Optimized Repairs -- 6 Evaluation -- 7 Conclusion -- References -- Generalized Completeness for SOS Resolution and its Application to a New Notion of Relevance -- 1 Introduction -- 2 Resolution Proof Transformation -- 3 A Generalized Completeness Proof for SOS -- 4 A new Notion of Relevance -- 5 Conclusion -- References -- A Unifying Splitting Framework -- 1 Introduction -- 2 Preliminaries -- 3 Splitting Calculi -- 4 Model-Guided Provers -- 5 Locking Provers -- 6 AVATAR-Based Provers -- 7 Application to Other Architectures -- 8 Conclusion -- Integer Induction in Saturation -- 1 Introduction -- 2 Motivating Examples -- 2.1 Preliminaries -- 2.2 Examples -- 3 Integer Induction -- 4 Integer Induction in Saturation-Based Proof Search -- 5 Implementation and Experiments -- 5.1 Implementation -- 5.2 Benchmarks -- 5.3 Experimental Setup -- 5.4 Experimental Results -- 6 Related Work -- 7 Conclusions |
| Title | Automated Deduction - CADE 28 |
| URI | http://digital.casalini.it/9783030798765 https://directory.doabooks.org/handle/20.500.12854/71322 https://library.oapen.org/handle/20.500.12657/50048 https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=6676599 |
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