Automated Deduction in Equational Logic and Cubic Curves

Automated Deduction in Equational Logic and Cubic Curves

Author: William McCune

Publisher: Springer Science & Business Media

Published: 1996-06-12

Total Pages: 248

ISBN-13: 9783540613985

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This monograph is the result of the cooperation of a mathematician working in universal algebra and geometry, and a computer scientist working in automated deduction, who succeeded in employing the theorem prover Otter for proving first order theorems from mathematics and then intensified their joint effort. Mathematicians will find many new results from equational logic, universal algebra, and algebraic geometry and benefit from the state-of-the-art outline of the capabilities of automated deduction techniques. Computer scientists will find a large and varied source of theorems and problems that will be useful in designing and evaluation automated theorem proving systems and strategies.


Equational Logic as a Programming Language

Equational Logic as a Programming Language

Author: Michael J. O'Donnell

Publisher: MIT Press (MA)

Published: 1985

Total Pages: 334

ISBN-13:

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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.


Iteration Theories

Iteration Theories

Author: Stephen L. Bloom

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 636

ISBN-13: 3642780342

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This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi nary facts in Chapter 1. Written both for graduate students and research scientists in theoret ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in finitary regular languages, trees, synchronization trees, 2-categories, and others.


Foundations of Equational Logic Programming

Foundations of Equational Logic Programming

Author: Steffen Hölldobler

Publisher: Lecture Notes in Artificial Intelligence

Published: 1989

Total Pages: 268

ISBN-13:

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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.


Foundations of Probabilistic Programming

Foundations of Probabilistic Programming

Author: Gilles Barthe

Publisher: Cambridge University Press

Published: 2020-12-03

Total Pages: 583

ISBN-13: 110848851X

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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.


Constraints in Computational Logics: Theory and Applications

Constraints in Computational Logics: Theory and Applications

Author: Hubert Comon

Publisher: Springer

Published: 2003-08-06

Total Pages: 321

ISBN-13: 3540454063

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Constraints provide a declarative way of representing infinite sets of data. They are well suited for combining different logical or programming paradigms as has been known for constraint logic programming since the 1980s and more recently for functional programming. The use of constraints in automated deduction is more recent and has proved to be very successful, moving the control from the meta-level to the constraints, which are now first-class objects. This monograph-like book presents six thoroughly reviewed and revised lectures given by leading researchers at the summer school organized by the ESPRIT CCL Working Group in Gif-sur-Yvette, France, in September 1999. The book offers coherently written chapters on constraints and constraint solving, constraint solving on terms, combining constraint solving, constraints and theorem proving, functional and constraint logic programming, and building industrial applications.


Constraints in Computational Logics. Theory and Applications

Constraints in Computational Logics. Theory and Applications

Author: Hubert Comon

Publisher: Springer Science & Business Media

Published: 2001-04-18

Total Pages: 321

ISBN-13: 3540419500

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Constraints and constraint solving : an introduction / Jean-Pierre Jouannaud / - Constraint solving on terms / Hubert Comon / - Combining constraint solving / Franz Baader / - Constraints and theorem proving / Harald Ganzinger / - Functional and constraint logic programming / Mario Rodríguez-Artalejo / - Building industrial applications with constraint programming / Helmut Simonis.