Recent work in Artificial Intelligence is exploring the use of formal ontologies as a way of specifying content-specific agreements for the sharing and reuse of knowledge among software entities. We take an engineering perspective on the development of such ontologies. Formal ontologies are viewed as designed artifacts, formulated for specific purposes and evaluated against objective design criteria. We describe the role of ontologies in supporting knowledge sharing activities, and then present a set of criteria to guide the development of ontologies for these purposes. We show how these criteria are applied in case studies from the design of ontologies for engineering mathematics and bibliographic data. Selected design decisions are discussed, and alternative representation choices and evaluated against the design criteria.

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Toward principles for the design of ontologies used for knowledge sharing

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.

Foundations of logic programming

From the Publisher:
An agent is an entity with domain knowledge, goals and actions. Multi-agent systems are a set of agents which
interact in a common environment. Multi-agent systems deal with the construction of complex systems involving multiple agents and their coordination. A multi-agent system (MAS) is a distributed computing system with
autonomous interacting intelligent agents that coordinate their actions so as to achieve its goal(s) jointly or competitively.

Introduction to Multiagent Systems

From the Publisher:
Since the introduction of Hoares' Communicating Sequential Processes notation, powerful new tools have transformed CSP into a practical way of describing industrial-sized problems. This book gives you the fundamental grasp of CSP concepts you'll need to take advantage of those tools.Part I provides a detailed foundation for working with CSP, using as little mathematics as possible. It introduces the ideas behind operational, denotational and algebraic models of CSP. Parts II and III go into greater detail about theory and practice. Topics include: parallel operators, hiding and renaming, piping and enslavement, buffers and communication, termination and sequencing, and semantic theory. Three detailed practical case studies are also presented.For anyone interested in modeling sequential processes.

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The Theory and Practice of Concurrency

We propose a novel formalism, called Frame Logic (abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the object-oriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts that come from object-oriented programming have direct representation in F-logic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive object-oriented language based on a subset of F-logic.

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Logical foundations of object-oriented and frame-based languages

USEFUL FACTS ABOUT SETS. SENTENTIAL LOGIC. FIRST-ORDER LOGIC. UNDECIDABILITY. SECOND-ORDER LOGIC.

A mathematical introduction to logic

Contents Preface List of Symbols Chapter 1 Introduction Baby Set Theory Sets-An Informal View Classes Axiomatic Method Notation Historical Notes Chapter 2 Axioms and Operations Axioms Arbitrary Unions and Intersections Algebra of Sets Epilogue Review Exercises Chapter 3 Relations and Functions Ordered Pairs Relations n-Ary Relations Functions Infinite Cartesian Products Equivalence Relations Ordering Relations Review Exercises Chapter 4 Natural Numbers Inductive Sets Peano's Postulates Recursion on Arithmetic Ordering on Review Exercises Chapter 5 Construction of the Real Numbers Integers Rational Numbers Real Numbers Summaries Two Chapter 6 Cardinal Numbers and the Axiom of Choice Equinumerosity Finite Sets Cardinal Arithmetic Ordering Cardinal Numbers Axiom of Choice Countable Sets Arithmetic of Infinite Cardinals Continuum Hypothesis Chapter 7 Orderings and Ordinals Partial Orderings Well Orderings Replacement Axioms Epsilon-Images Isomorphisms Ordinal Numbers Debts Paid Rank Chapter 8 Ordinals and Order Types Transfinite Recursion Again Alephs Ordinal Operations Isomorphism Types Arithmetic of Order Types Ordinal Arithmetic Chapter 9 Special Topics Well-Founded Relations Natural Models Cofinality Appendix Notation, Logic, and Proofs Selected References for Further Study List of Axioms Index

Elements of Set Theory

The journal of symbolic logic began publishing in 1936. From the outset, the JOURNAL included a Reviews Section, edited by Alonzo Church. The very first issue carried three pages of reviews, written by Bernays, Church, Rosser, and Quine. As the first issue stated, "It is intended that this section of the JOURNAL shall serve as a complete bibliography of current literature in the field of symbolic logic, from January 1, 1936. To this end an effort will be made to include in it, at least by title, all publications in this field, both books and articles in journals, and as far as possible these will be accompanied by signed reviews." Thus the purpose of the Reviews Section was twofold. For one, there was its bibliographical function: to provide a complete, suitably indexed, listing of all the publications-both books and journal articles-in symbolic logic, wherever and in whatever language published. And secondly, the reviews were to provide critical, analytical commentary on these publications, whenever possible. The Reviews Section should be viewed as a continuation and expansion of Church's A bibliography of symbolic logic. The Bibliography was a listing, with some annotations, of the publications in symbolic logic prior to 1936. It was published as volume 1, number 4 of the JOURNAL. Church made the listing as complete as he could, of course. When additional pre-1936 publications came to his attention, they were initially added to the Additions and corrections, published in volume 3, pages 178-192; the ones found later were listed in the Reviews Section. (In 1984, the Bibliography was reissued, together with the Additions and corrections and the subsequently discovered items. The reissue is therefore the authoritative listing of publications in symbolic logic prior to 1936.) Assembling the Bibliography required Church to formulate principles as to exactly what "symbolic logic" was or was not. The field was not simply logic-there are still works published with 'logic' in their titles but which make no use of formal or mathematical methods. Church drew the starting line at Leibniz's 1666 work, Dissertatio de arte combinatoria in qua ex

Alonzo Church and the Reviews

Computability Theory: An Introduction to Recursion Theory, provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way. Frequent historical information presented throughout More extensive motivation for each of the topics than other texts currently available Connects with topics not included in other textbooks, such as complexity theory

Herbert B. Enderton

Papers

A mathematical introduction to logic

Elements of Set Theory

Alonzo Church and the Reviews

Computability Theory: An Introduction to Recursion Theory

Chapter TWO – First-Order Logic