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Author: Steffen Hölldobler
Publisher: Lecture Notes in Artificial Intelligence
ISBN:
Category : Computers
Languages : en
Pages : 264
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Book Description
Equations play a vital role in many fields of mathematics, computer science, and artificial intelligence. Therefore, many proposals have been made to integrate equational, functional, and logic programming. This book presents the foundations of equational logic programming. After generalizing logic programming by augmenting programs with a conditional equational theory, the author defines a unifying framework for logic programming, equation solving, universal unification, and term rewriting. Within this framework many known results are developed. In particular, a presentation of the least model and the fixpoint semantics of equational logic programs is followed by a rigorous proof of the soundness and the strong completeness of various proof techniques: SLDE-resolution, where a universal unification procedure replaces the traditional unification algorithm; linear paramodulation and special forms of it such as rewriting and narrowing; complete sets of transformations for conditional equational theories; and lazy resolution combined with any complete set of inference rules for conditional equational theories.
Author: Steffen Hölldobler
Publisher: Lecture Notes in Artificial Intelligence
ISBN:
Category : Computers
Languages : en
Pages : 264
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Book Description
Equations play a vital role in many fields of mathematics, computer science, and artificial intelligence. Therefore, many proposals have been made to integrate equational, functional, and logic programming. This book presents the foundations of equational logic programming. After generalizing logic programming by augmenting programs with a conditional equational theory, the author defines a unifying framework for logic programming, equation solving, universal unification, and term rewriting. Within this framework many known results are developed. In particular, a presentation of the least model and the fixpoint semantics of equational logic programs is followed by a rigorous proof of the soundness and the strong completeness of various proof techniques: SLDE-resolution, where a universal unification procedure replaces the traditional unification algorithm; linear paramodulation and special forms of it such as rewriting and narrowing; complete sets of transformations for conditional equational theories; and lazy resolution combined with any complete set of inference rules for conditional equational theories.
Author: Steffen Holldobler
Publisher:
ISBN: 9783662162132
Category :
Languages : en
Pages : 268
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Book Description
Author: Michael J. O'Donnell
Publisher: MIT Press (MA)
ISBN:
Category : Computers
Languages : en
Pages : 334
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Book Description
This book describes an ongoing equational programming project that started in 1975. Within the project an equational programming language interpreter has been designed and implemented. The first part of the text (Chapters 1-10) provides a user's manual for the current implementation. The remaining sections cover the following topics: programming techniques and applications, theoretical foundations, implementation issues. Giving a brief account of the project's history (Chapter 11), the author devotes a large part of the text to techniques of equational programming at different levels of abstraction. Chapter 12 discusses low-level techniques including the distinction of constructors and defined functions, the formulation of conditional expressions and error and exception handling. High-level techniques are treated in Chapter 15 by discussing concurrency, nondeterminism, the relationship to dataflow programs and the transformation of recursive programs called dynamic programming. In Chapter 16 the author shows how to efficiently implement common data structures by equational programs. Modularity is discussed in Chapter 14. Several applications are also presented in the book. The author demonstrates the versatility of equational programming style by implementing syntactic manipulation algorithms (Chapter 13). Theoretical foundations are introduced in Chapter 17 (term rewriting systems, herein called term reduction systems). In Chapter 19 the author raises the question of a universal equational machine language and discusses the suitability of different variants of the combinator calculus for this purpose. Implementation issues are covered in Chapters 18 and 20 focused around algorithms for efficient pattern matching, sequencing and reduction. Aspects of design and coordination of the syntactic processors are presented as well.
Author: Jack Minker
Publisher: Morgan Kaufmann
ISBN: 1483221121
Category : Computers
Languages : en
Pages : 753
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Book Description
Foundations of Deductive Databases and Logic Programming focuses on the foundational issues concerning deductive databases and logic programming. The selection first elaborates on negation in logic programming and towards a theory of declarative knowledge. Discussions focus on model theory of stratified programs, fixed point theory of nonmonotonic operators, stratified programs, semantics for negation in terms of special classes of models, relation between closed world assumption and the completed database, negation as a failure, and closed world assumption. The book then takes a look at negation as failure using tight derivations for general logic programs, declarative semantics of logic programs with negation, and declarative semantics of deductive databases and logic programs. The publication tackles converting AND-control to OR-control by program transformation, optimizing dialog, equivalences of logic programs, unification, and logic programming and parallel complexity. Topics include parallelism and structured and unstructured data, parallel algorithms and complexity, solving equations, most general unifiers, systems of equations and inequations, equivalences of logic programs, and optimizing recursive programs. The selection is a valuable source of data for researchers interested in pursuing further studies on the foundations of deductive databases and logic programming.
Author: Steffen Hölldobler
Publisher: Lecture Notes in Artificial Intelligence
ISBN:
Category : Computers
Languages : en
Pages : 268
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Book Description
Equations play a vital role in many fields of mathematics, computer science, and artificial intelligence. Therefore, many proposals have been made to integrate equational, functional, and logic programming. This book presents the foundations of equational logic programming. After generalizing logic programming by augmenting programs with a conditional equational theory, the author defines a unifying framework for logic programming, equation solving, universal unification, and term rewriting. Within this framework many known results are developed. In particular, a presentation of the least model and the fixpoint semantics of equational logic programs is followed by a rigorous proof of the soundness and the strong completeness of various proof techniques: SLDE-resolution, where a universal unification procedure replaces the traditional unification algorithm; linear paramodulation and special forms of it such as rewriting and narrowing; complete sets of transformations for conditional equational theories; and lazy resolution combined with any complete set of inference rules for conditional equational theories.
Author: Christian Prehofer
Publisher: Springer Science & Business Media
ISBN: 1461217784
Category : Computers
Languages : en
Pages : 193
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Book Description
This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica tions, higher-order logic provides the necessary level of abstraction for con cise and natural formulations. The main assets of higher-order logic are quan tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.
Author: Gilles Barthe
Publisher: Cambridge University Press
ISBN: 110848851X
Category : Computers
Languages : en
Pages : 583
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Book Description
This book provides an overview of the theoretical underpinnings of modern probabilistic programming and presents applications in e.g., machine learning, security, and approximate computing. Comprehensive survey chapters make the material accessible to graduate students and non-experts. This title is also available as Open Access on Cambridge Core.
Author: Răzvan Diaconescu
Publisher:
ISBN: 9780902928916
Category : Categories (Mathematics)
Languages : en
Pages : 120
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Book Description
Abstract: "This thesis proposes a general framework for equational logic programming, called category-based equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic category-based approach to a paramodulation- based operational semantics for equational logic programming languages. Category-based equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports in the context of a category-based semantics for solutions to equational logic programming queries. Constraint logic programming is integrated into the equational logic programming paradigm by showing that constraint logics are a particular case of category-based equational logic. This follows the methodology of free expansions of models for built-ins along signature inclusions as sketched by Goguen and Meseguer in their papers on Eqlog. The mathematical foundations of constraint logic programming are based on a Herbrand Theorem for constraint logics; this is obtained as an instance of a more general category-based version of Herbrand's Theorem. The results in this thesis apply to equational and constraint logic programming languages that are based on a variety of equational logical systems including many and order sorted equational logics, Horn clause logic, equational logic modulo a theory, constraint logics, and more, as well as any possible combination between them. More importantly, this thesis gives the possibility for developing the equational logic (programming) paradigm over non-conventional structures and thus significantly extending it beyond its tradition."
Author: Sergei Artemov
Publisher: Springer
ISBN: 3642357229
Category : Mathematics
Languages : en
Pages : 424
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Book Description
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2013, held in San Diego, CA, USA in January 2013. The volume presents 29 revised refereed papers carefully selected by the program committee. The scope of the Symposium is broad and includes constructive mathematics and type theory; logic, automata and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logic; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple agent system logics; logics of proof and justification; nonmonotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
Author: Hélène Kirchner
Publisher: Springer Science & Business Media
ISBN: 9783540558736
Category : Computers
Languages : en
Pages : 476
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Book Description
This volume contains the proceedings of the Third International Conference on Algebraic and Logic Programming, held in Pisa, Italy, September 2-4, 1992. Like the two previous conferences in Germany in 1988 and France in 1990, the third conference aims at strengthening the connections betweenalgebraic techniques and logic programming. On the one hand, logic programming has been very successful during the last decades and more and more systems compete in enhancing its expressive power. On the other hand, concepts like functions, equality theory, and modularity are particularly well handled in an algebraic framework. Common foundations of both approaches have recently been developed, and this conference is a forum for people from both areas to exchange ideas, results, and experiences. The book covers the following topics: semantics ofalgebraic and logic programming; integration of functional and logic programming; term rewriting, narrowing, and resolution; constraintlogic programming and theorem proving; concurrent features in algebraic and logic programming languages; and implementation issues.
