
Logic for Programming, Artificial Intelligence, and Reasoning
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Content
- Title
- Preface
- Organisation
- Table of Contents
- The TPTP World - Infrastructure for Automated Reasoning
- Introduction
- The TPTP World Core Infrastructure
- TPTP World Services
- TPTP World Applications
- Current Developments in the TPTP World
- Conclusion
- References
- Speed-Up Techniques for Negation in Grounding
- Introduction
- Background
- Formula Rewriting
- T/F Relational Algebra
- Comparing the Methods: An Example
- Experimental Evaluation
- Conclusions and Future Work
- References
- Constraint-Based Abstract Semantics for Temporal Logic: A Direct Approach to Design and Implementation
- Introduction
- Preliminaries
- Semantics of -Calculus
- CTL Syntax and Semantics
- Model Checking
- Abstract Interpretation
- Abstract Interpretation of -Calculus Semantics
- An Abstract Constraint-Based Domain
- Abstract Domains Based on a State-Space Partitions
- Constraint Representation of Transition Systems
- Constraint Representation of the Semantic Functions
- Implementation
- Computation of and Functions Using Constraint Solvers
- Optimisation of Constraint-Based Evaluation
- Experiments Using an SMT Constraint Solver
- Property-Specific Refinements
- Related Work
- Conclusion
- References
- On the Equality of Probabilistic Terms
- Introduction
- A Motivating Example
- Preliminaries
- Syntax and Semantics
- Syntax
- Semantics
- Satisfaction Problem
- Exclusive or, Concatenation, and Projection
- Exclusive or
- Exclusive or, Concatenation, and Projection
- An Equational Logic for Systems of Equations
- Proof System
- Soundness
- Products
- Example Revisited
- Towards Completeness
- Proof Automation
- Conclusion
- References
- Program Logics for Homogeneous Meta-programming
- Introduction
- The Language
- A Logic for Total Correctness
- Reasoning Examples
- Completeness
- Conclusion
- References
- Verifying Pointer and String Analyses with Region Type Systems
- Introduction
- Featherweight Java with Updates
- Preliminaries
- Syntax
- Semantics
- Class Tables
- Region Type System
- Refined Types and Subtyping
- Annotated Class Tables
- Region Type System
- Interpretation
- Parametrized Region Type System
- Abstraction Principles
- The Parametrized Type System
- Algorithmic Type Checking
- String Analysis
- FJEU with Strings
- Pointer Analysis for String Objects
- String Analysis with Operation Contexts
- Discussion
- References
- ABC: Algebraic Bound Computation for Loops
- Introduction
- Motivating Examples
- ABC: System Description
- ABC-Loops
- The Loop Converter
- The Bound Computer
- Symbolic Solver
- Beyond ABC-Loops
- Experiments
- Conclusions
- References
- Hardness of Preorder Checking for Basic Formalisms
- Introduction
- Preliminaries
- Exptime-Hardness of Problems 1 and 2
- Exptime-Hardness of Problem 1
- Exptime-Hardness of Problem 2
- Additional Hardness Results
- Conclusions
- References
- A Quasipolynomial Cut-Elimination Procedure in Deep Inference via Atomic Flows and Threshold Formulae
- Introduction
- Propositional Logic in Deep Inference: The SKS System
- Atomic Flows
- Normalisation Step 1: Simple Form
- Threshold Formulae
- Normalisation Step 2: Cut Elimination
- Final Comments
- References
- Pairwise Cardinality Networks
- Introduction
- Sorting Networks - From Batcher to Parberry
- Sorting Networks - From Parberry Back to Batcher
- The Pairwise Cardinality Network
- A Preliminary Evaluation
- Summary and Conclusion
- References
- Logic and Computation in a Lambda Calculus with Intersection and Union Types
- Introduction
- Intersection and Union Types
- $\UNINTU$ : Curry-Style Type Assignment with Intersections and Unions
- $\UNINT$: Church-Style Typing with Intersections and Unions
- The Proof-Term Calculus $\PROOFIU$
- Typed Terms with Intersections and Unions
- Example of Typing for $\UNINT$
- The Isomorphism between $\UNINTU$ and $\UNINT$
- Type Reconstruction and Type Checking Algorithms
- Reduction in $\UNINT$
- Synchronization
- The Reduction Relation $\churchred$
- Example of Reduction for $\UNINT$ (Continued)
- Properties of $\churchred$
- Deciding Type-Derivation Equality
- Type Theories
- Future Work
- References
- Graded Alternating-Time Temporal Logic
- Introduction
- A Motivating Example
- Preliminaries
- Graded ATL: Definitions
- Fixpoint Characterization
- Comparing the Semantics
- Model Checking
- Model Checking Concurrent Games
- References
- Non-oblivious Strategy Improvement
- Introduction
- Preliminaries
- Snares
- Strategy Improvement
- Strategy Trees
- Profitable Back Edges
- Using Snares to Guide Strategy Improvement
- Comparison with Oblivious Strategy Improvement
- Optimal Switching Policies
- Friedmann's Exponential Time Examples
- Conclusions and Further Work
- References
- A Simple Class of Kripke-Style Models in Which Logic and Computation Have Equal Standing
- Introduction
- The Models, Computation, Logic
- Frames
- $\lambda$-Terms
- The Logic
- Expressivity
- Completeness for $\lambda$-Reduction
- The Axioms, Soundness and Completeness
- Theorems and Admissible Rules
- Soundness
- Completeness
- Conclusion
- Negation and the Liar
- Related Work
- Summary, and Further Work
- References
- Label-Free Proof Systems for IntuitionisticModal Logic $\is$
- Introduction
- The Intuitionistic Modal Logic $\is$
- Label-Free Natural Deduction for $\is$
- The MC-Sequent Structure
- A Natural Deduction System for $\is$
- Natural Deduction Systems for $\sff$ and $\imf$
- A Label-Free Sequent Calculus for $\is$
- Depth-Preserving Admissibility of Weakening and Contraction
- Cut-Elimination in $\gis$
- A New Decision Procedure for $\is$
- Conclusion and Perspectives
- References
- An Intuitionistic Epistemic Logic for Sequential Consistency on Shared Memory
- Introduction
- Intuitionistic Epistemic Logic for Asynchronous Communication
- Syntax
- Semantics
- Soundness
- Strong Completeness
- Axiom Type for Sequential Consistency
- Soundness
- Strong Completeness
- Waitfree Computation
- Decidability of Solvability of Waitfree Task Specification
- Related Work
- Discussions
- References
- Disunification for Ultimately Periodic Interpretations
- Introduction
- Preliminaries
- Disunification
- The Disunification Algorithm PDU
- Correctness and Termination
- Predicate Completion
- Decidability of the Satisfiability of Equational Formulae
- Implementation
- Conclusion
- References
- Synthesis of Trigger Properties
- Introduction
- Trigger Logic
- Automata onWords and Trees
- Expressiveness
- Synthesis
- Upper Bound
- Lower Bound
- Practice Issues
- References
- Semiring-Induced Propositional Logic: Definition and Basic Algorithms
- Introduction
- Semirings
- Semiring-Induced Propositional Logic
- Syntax
- Semantics
- Applications
- Decision Problems (Abool)
- Summation Problems (Acount)
- Optimization Problems (Amin+, Amax)
- Multi-criteria Optimization Problems (An, Af)
- A DPLL Algorithm for Semiring-Induced Propositional Logic
- Transition Systems
- States in SDPLL Transition Systems
- The Basic SDPLL Procedure
- Extending SAT Techniques
- Backjumping, Learning and Restarts
- Conflict-Driven Backjumping and Learning
- Semirings with Idempotent
- Conclusions and Future Work
- References
- Dafny: An Automatic Program Verifier for Functional Correctness
- Introduction
- Dafny Language Features
- Types
- Pre- and Postconditions
- Ghost State
- Modifications
- Functions
- Specifying Data-Structure Invariants
- Type Parameters
- Sets
- Sequences
- Algebraic Datatypes
- Termination Metrics
- Case Study: Schorr-Waite Algorithm
- Related Work
- Conclusions
- References
- Relentful Strategic Reasoning in Alternating-Time Temporal Logic
- Introduction
- Preliminaries
- Memoryful Alternating-Time Temporal Logic
- Decision Procedures
- Agent-Action Tree Automata with Satellites
- From Path Formulas to Satellites
- Satisfiability
- Model Checking
- References
- Counting and Enumeration Problems with Bounded Treewidth
- Introduction
- Preliminaries
- Counting Problems
- Enumeration Problems
- 3-Colorability
- Conclusion
- References
- The Nullness Analyser of {\sc{julia}}
- Introduction
- An Introductory Example
- Nullness Analysis in {\sc{julia}}
- Nullness Analysis of Local Variables
- Globally non-null Fields
- Locally non-null Fields
- Full Arrays
- Collection Classes
- Construction of the Annotation File
- Conclusion
- References
- Qex: Symbolic SQL Query Explorer
- Introduction
- Preliminaries
- Equational Axioms over Lists
- Equational Axioms and E-Matching in SMT Solvers
- Axioms over Lists
- From SQL to Formulas
- Tables and Table Constraints
- Nullable Values
- Formulas for Queries
- Implementation
- Incremental Table Generation
- Symmetry Breaking Formulas
- Experiments
- Related Work
- Conclusion and Future Work
- References
- Automated Proof Compression by Invention of New Definitions
- Introduction, Motivation, and Related Work
- Problem Statement
- Problem of Proof Compression by New Definitions
- Motivating Example
- Implementation
- The Most Compressing Definition and the Least General Generalization
- Finding the Most Compressing Definition Using Substitution Trees
- Testing
- Testing on the TPTP Library
- Testing on Algebraic Problems
- Examples and Discussion
- A Good and a Bad Example
- Understanding Machine Generated Proofs
- Future Work and Conclusions
- References
- Atomic Cut Introduction by Resolution: Proof Structuring and Compression
- Introduction
- The Sequent Calculus
- TheCIRes Method
- Step 1: Introduction of Atomic Cuts on Top
- Step 2: Extraction of the Struct
- Step 3: Construction of the Swapped Clause Set
- Step 4: Refutation of the Swapped Clause Set by Resolution
- Step 5: Construction of O-Projections
- Step 6: Composing the O-Projections on Top of the Refutation
- Exponential Proof Compression
- Conclusions
- References
- Satisfiability of Non-linear (Ir)rational Arithmetic
- Introduction
- Encoding Non-linear Non-integral Arithmetic
- Rational Arithmetic
- Extending Rational Arithmetic by Roots of Numbers
- Experimental Evaluation
- Comparison with SMT Solvers
- Evaluation within a Termination Prover
- Related Work and Concluding Remarks
- References
- Coping with Selfish On-Going Behaviors
- Introduction
- Preliminaries
- Weighted Finite Automaton
- Input Cheating and Resilience of Automata
- The Cheating-Allowed Automaton
- Resilience Testing
- Hardness Proof for WFA
- A Polynomial Algorithm for DWFA
- Achieving Resilience with Minimum Resources
- Hardness Proof for WFA
- A Polynomial Algorithm for DWFA
- References
- Author Index
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