Keywords:
Artificial intelligence.
;
Computer logic.
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Automatisches Beweisverfahren.-gnd-(DE-588)4069034-9.
;
Mathematik.-gnd-(DE-588)4037944-9.
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Electronic books.
Description / Table of Contents:
This Festschrift volume is published in honor of William W. McCune, an accomplished computer scientist who was a fantastic system builder and software engineer. It includes 13 papers that cover automated reasoning and its applications to mathematics.
Type of Medium:
Online Resource
Pages:
1 online resource (276 pages)
Edition:
1st ed.
ISBN:
9783642366758
Series Statement:
Lecture Notes in Computer Science Series ; v.7788
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=3093552
DDC:
006.3
Language:
English
Note:
Cover -- Title -- Table of Contents -- The Legacy of a Great Researcher -- Perspective and Genesis -- Combinatory Logic -- Boolean Algebra -- Logic Calculi and More Enhancements -- Group Theory -- Other Areas of Abstract Algebra -- Introducing Bill McCune -- References -- The Strategy Challenge in SMT Solving -- Introduction -- Caveat Emptor: What This Paper Is and Is Not -- Overview -- Strategy in Mechanized Proof -- What is Strategy? -- Strategy in Automated Theorem Proving over FOL -- Strategy in LCF-Style Interactive Proof Assistants -- Foundations for Big-Step Strategies -- Parametric Reasoning Engines as Tacticals -- Strategies in Action -- Z3 QF_LIA Strategy -- Calculemus RAHD Strategies -- Conclusion -- References -- Simple and Efficient Clause Subsumptionwith Feature Vector Indexing -- Introduction -- Preliminaries -- Subsumption -- Subsumption Variants -- Saturation Procedures and Clause Set Subsumption -- Feature Vector Indexing -- Subsumption-Compatible Clause Features -- Clause Feature Vectors and Candidate Sets -- Index Data Structure -- Forward Subsumption -- Backward Subsumption -- Optimizing the Index Data Structure -- Implementation Notes -- Experimental Results -- Prover Instrumentation and Configuration -- Feature Selection -- Feature Vector Optimization -- Basic Performance -- Profiling and Time Behavior -- Performance in Automatic Mode -- Future Work -- Conclusion -- References -- Superposition for Bounded Domains -- Introduction -- Getting Started -- A Calculus for T-unsatisfiability -- Calculus Rules -- Redundancy in SB and in S -- Application to Unit Rewriting -- Obtaining a Decision Procedure -- Calculus Rules -- Soundness and Refutational Completeness -- Termination by Loop Detection -- Termination by Rewriting -- Extensions -- Combinations with Unbounded First-Order Theories -- Three Application Scenarios.
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Combination with Theories -- Vectors over Finite Domains -- Proof Obligations from ISABELLE -- Conclusion and Future Work -- References -- MACE4 and SEM: A Comparison of Finite Model Generators -- Introduction -- Model Generation: Basic Concepts and Notations -- Two Small Examples -- Input of Mace4 and SEM -- Preprocessing -- Basic Search Algorithm in Mace4 and SEM -- A Backtracking Search Procedure -- Avoiding Search for Isomorphic Models -- Selecting Cells -- Constraint Propagation -- Simplification Rules -- Inference Rules -- Empirical Evaluation -- Algebra and Logic -- Quasigroup Problems -- Experimental Results -- A Challenging Latin Square Problem -- Basic Concepts -- Specification of (3,2,1)-ICODLS(11,3) -- Construction of (3,2,1)-ICODLS(11,3) -- Conclusion and Future Works -- References -- Group Embedding of the Projective Plane PG(2, 3) -- Bill McCune -- Finite Projective Planes as Groups -- The Procedure for Group Embedding of PG(2,3). -- An Example of an Impossibility Proof -- Prover9 Steps -- References -- A Geometric Procedure with Prover9 -- In Memory of Bill McCune -- A First-Order Property for Cubic Curves -- Implementing gL in Prover9 -- Group Law on Non-singular Cubic Curves -- Conclusion -- References -- Loops with Abelian Inner Mapping Groups: An Application of Automated Deduction -- Introduction -- The Main Conjecture and the Project -- The Strategy -- LC Loops -- Further Remarks -- References -- (Dual) Hoops Have Unique Halving -- Introduction -- The Logics -- Algebraic Semantics -- Automated Proofs and Counterexamples -- Subsequent Work -- Final Remarks -- References -- Gibbard's Collapse Theorem for the Indicative Conditional: An Axiomatic Approach -- Background: Gibbard's (Informal) Argument -- Axiomatization of the Gibbardian Collapse Phenomenon -- Concluding Remarks -- Appendix: Proofs of Theorems.
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Proofs of the Independence of Our Axioms (1)-(8) -- Proof of Our (Intuitionistic) Collapse Theorem -- Counterexample to Peirce's Law for and -- References -- Geometric Quantifier Elimination Heuristics for Automatically Generating Octagonal and Max-plus Invariants -- Introduction -- Related Work -- On the Quality of Invariants Generated Using Quantifier Elimination -- Octagonal Invariants -- Overview -- Program Analysis Using Octagonal Invariants -- Trivially Redundant and Implicit Conditions -- Localized Quantifier Elimination -- Geometric View of Quantifier Elimination -- Reversal of the Signs of Both Variables -- The Signs of Both Variables Remain Invariant -- The Sign of Exactly One Variable Is Reversed -- The Effects of Computing the Closure of the Tests and Choosing Different Table Entries -- Programs with Multiple Loops -- Strongest Invariants and Complexity -- Invariant Generation with Max-plus Polyhedra -- Invariant Generation -- Concluding Remarks and Future Work -- References -- Toward a Procedure for Data Mining Proofs -- Introduction -- Proof Sketches -- Applications of Mutual Information -- Mutual Information -- Applications of Mutual Information -- Experimental Results -- Boolean Algebra -- Field Theory -- Group Theory -- Conclusion -- References -- Theorem Proving in Large Formal Mathematics as an Emerging AI Field -- OTTER and QED -- Why Link Large Formal Mathematics with AI/ATP Methods? -- Why Mizar? -- MPTP: Translating Mizar for Automated Reasoning Tools -- Experiments and Projects Based on the MPTP -- Re-proving Experiments -- Finding New Proofs and the AI Aspects -- ATP-Based Explanation, Presentation, and Cross-verification of Mizar Proofs -- Use of MPTP for ATP Challenges and Competitions -- Development of Larger AI Metasystems Like MaLARea and MaLeCoP on MPTP Data -- Future QED-Like Directions -- References -- Author Index.
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