Author

# Krzysztof R. Apt

Other affiliations: University of Paris, Erasmus University Rotterdam, University of Texas at Austin ...read more

Bio: Krzysztof R. Apt is an academic researcher from Centrum Wiskunde & Informatica. The author has contributed to research in topics: Logic programming & Constraint programming. The author has an hindex of 46, co-authored 315 publications receiving 15936 citations. Previous affiliations of Krzysztof R. Apt include University of Paris & Erasmus University Rotterdam.

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01 Jan 1992

Abstract: Publisher Summary
This chapter focuses on logic programming, which is closely related to PROLOG. Logic programming constitutes the theoretical framework of PROLOG. This close connection led to the adoption of logic programming as the basis for the influential Japanese Fifth Generation Project. The power of logic programming stems from two reasons. First, it is an extremely simple formalism. It also relies on mathematical logic, which developed its own methods and techniques and which provides a rigorous mathematical framework. The chapter presents a self-contained introduction to the theory of logic programming. It also discusses the causal dependence between various concepts and notions and presents the notion of SLD-resolution, which is central to the subject of logic programming.

1,735 citations

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01 Jan 1990TL;DR: This chapter presents a self-contained introduction to the theory of logic programming, which discusses the causal dependence between various concepts and notions and presents the notion of SLD-resolution, which is central to the subject of logic Programming.

Abstract: Publisher Summary
This chapter focuses on logic programming, which is closely related to PROLOG. Logic programming constitutes the theoretical framework of PROLOG. This close connection led to the adoption of logic programming as the basis for the influential Japanese Fifth Generation Project. The power of logic programming stems from two reasons. First, it is an extremely simple formalism. It also relies on mathematical logic, which developed its own methods and techniques and which provides a rigorous mathematical framework. The chapter presents a self-contained introduction to the theory of logic programming. It also discusses the causal dependence between various concepts and notions and presents the notion of SLD-resolution, which is central to the subject of logic programming.

1,659 citations

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01 Aug 1988

TL;DR: This work proves the consistency of Clark's completion for stratified programs and attempts to clarify the sources of some previously reported difficulties with negation in logic programming.

Abstract: We identify a useful class of logic programs with negation, called stratified programs, that disallow certain combinations of recursion and negation. Programs in this class have a simple declarative and procedural meaning based, respectively, on model theory and a back-chaining interpreter. The standard model of a stratified program, which gives the program a declarative meaning and is independent of the stratification, is characterized in two ways. One is based on a fixed point theory of nonmonotonic operators and the other on an abstract declarative characterization. The back-chaining interpreter also determines the standard model. Finally, we prove the consistency of Clark's completion for stratified programs and attempt to clarify the sources of some previously reported difficulties with negation in logic programming.

1,370 citations

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01 Jan 2003

TL;DR: Constraint programming combines ideas from artificial intelligence, programming languages, databases, and operational research as mentioned in this paper, and it has been widely used in the field of software engineering and management.

Abstract: Scheduling, vehicle routing and timetabling are all examples of constraint problems, and methods to solve them rely on the idea of constraint propagation and search. This book meets the need for a modern, multidisciplinary introduction to the field that covers foundations and applications. Written by Krzysztof Apt, an authority on the subject, it will be welcomed by graduate students and professionals. With the insertion of constraint techniques into programming environments, new developments have accelerated the solution process. Constraint programming combines ideas from artificial intelligence, programming languages, databases, and operational research.

730 citations

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TL;DR: It is shown that nondeterministic flowchart schemata of bounded nondeterminacy are modeled by this special case of Hom clauses, and the connection between finite failure and greatest fixpoint is used to give a semantic characterization of termination, blocking, and nontermination of such flowchart Schemata.

Abstract: Hom clauses of first-order predicate logic can be regarded as a high-level programming language when SLD-resolution, a special-purpose resolution theorem prover, is used as interpreter. Consequently, the semantics of Hom clauses can be studied both by model-theoretic and fixpoint methods (in the sense of Scott). This possibility is exploited here by identifying the least (greatest) fixpoint with a least (greatest) model. Successful termination of SLD-resolution is characterized by least fupoints. A semantic characterization of finite failure of SLD-resolution is given, which coincides with the greatest fixpoint only for a special case of clauses. It is shown that nondeterministic flowchart schemata of bounded nondeterminacy are modeled by this special case; the connection between finite failure and greatest fixpoint is then used to give a semantic characterization of termination, blocking, and nontermination of such flowchart schemata.

637 citations

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25 Apr 2008

TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.

Abstract: Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

4,905 citations

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01 Jan 1984TL;DR: This is the second edition of an account of the mathematical foundations of logic programming, which collects, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers.

Abstract: This is the second edition of an account of the mathematical foundations of logic programming. Its purpose is to collect, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples and problems. The text is intended to be self-contained, the only prerequisites being some familiarity with PROLOG and knowledge of some basic undergraduate mathematics. The material is suitable either as a reference book for researchers or as a textbook for a graduate course on the theoretical aspects of logic programming and deductive database systems.

4,500 citations

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TL;DR: By showing that argumentation can be viewed as a special form of logic programming with negation as failure, this paper introduces a general logic-programming-based method for generating meta-interpreters for argumentation systems, a method very much similar to the compiler-compiler idea in conventional programming.

4,386 citations

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01 Jan 2001

TL;DR: This chapter discusses Decision-Theoretic Foundations, Game Theory, Rationality, and Intelligence, and the Decision-Analytic Approach to Games, which aims to clarify the role of rationality in decision-making.

Abstract: Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

3,569 citations