R-Calculus, IV: Propositional Logic


Book Description

This fourth volume of the book series combines propositional logic and R-calculus for a new point of view to consider belief revision. It gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming, ⇝-propositional logic, semantic networks, and three-valued logic, etc.. Applications of R-calculus in logic of supersequents are also given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.




R-Calculus, II: Many-Valued Logics


Book Description

This second volume of the book series shows R-calculus is a combination of one monotonic tableau proof system and one non-monotonic one. The R-calculus is a Gentzen-type deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. It discusses the algebraical and logical properties of tableau proof systems and R-calculi in many-valued logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.




R-CALCULUS: A Logic of Belief Revision


Book Description

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.







Knowledge Science, Engineering and Management


Book Description

​This book constitutes the refereed proceedings of the 10th International Conference on Knowledge Science, Engineering and Management, KSEM 2017, held in Melbourne, Australia, in August 2017. The 35 revised full papers and 12 short papers presented were carefully reviewed and selected from 134 submissions. The papers are organized in the following topical sections: text mining and document analysis; formal semantics and fuzzy logic; knowledge management; knowledge integration; knowledge retrieval; recommendation algorithms and systems; knowledge engineering; and knowledge representation and reasoning.




The Logical Writings of Karl Popper


Book Description

This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.




Collected Papers of Stig Kanger with Essays on his Life and Work


Book Description

Stig Kanger (1924-1988) made important contributions to logic and formal philosophy. Kanger's dissertation Provability in Logic, 1957, contained significant results in proof theory as well as the first fully worked out model-theoretic interpretation of quantified modal logic. It is generally accepted nowadays that Kanger was one of the originators of possible worlds semantics for modal logic. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. He also contributed to action theory, preference logic, and the theory of measurement. This is the first of two volumes dedicated to the work of Stig Kanger. The present volume is a complete collection of Kanger's philosophical papers. The second volume contains critical essays on Kanger's work, as well as biographical essays on Kanger written by colleagues and friends.




Discrete Mathematics


Book Description

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.




Logical Studies


Book Description

First published in 2000. In this volume are eight essays; with the first three essays deal with the problem of logical truth. Their aim is to elucidate what is meant by saying that logical truth is formal-dependent of form and independent of content-or that logical truth is tautologous. The next is on study of distributive normal forms that awakened my interest in modality. The next three essays are in the field of modal logic. Related to modal logic are the problems of the conditional (the if-then) and of entailment (logical consequence) on which the final essay is based.