1 edition of **A Proof Theory for Description Logics** found in the catalog.

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Published
**2012** by Springer London in London .

Written in English

- Mathematical Logic and Formal Languages,
- Mathematics of Computing,
- Computer science

**Edition Notes**

Statement | by Alexandre Rademaker |

Series | SpringerBriefs in Computer Science |

Contributions | SpringerLink (Online service) |

The Physical Object | |
---|---|

Format | [electronic resource] / |

ID Numbers | |

Open Library | OL27083430M |

ISBN 10 | 9781447140023 |

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A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi.

The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes/5(2). A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi.

The author argues that such systems can improve the extraction of A Proof Theory for Description Logics book content from DLs proofs for explanation : Springer-Verlag London. A Proof Theory for Description Logics introduces Sequent A Proof Theory for Description Logics book and Natural Deduction for some DLs (ALC, ALCQ).

Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes. A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ).

Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction A Proof Theory for Description Logics book computational content from DLs proofs for explanation : Springer London.

A Proof Theory for Description Logics Thesis (PDF Available) January with 64 Reads How we measure 'reads' A 'read' is counted each time someone views a A Proof Theory for Description Logics book summary Author: Alexandre Rademaker.

Rademaker, Alexandre; Haeusler, Edward Hermann. A Proof Theory for Description Logics. Rio de Janeiro, p. DSc Thesis | Departamento de Inform atica, Pontif cia Universidade Cat olica do Rio de Janeiro. Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain.

They are equipped with a formal logic-based semantics. Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics/5(4).

Troelstra's Basic Proof Theory is a lightweight introductory text, but it does not treat the incompleteness results, and even worse, propositions-as-types. If you are interested in the proof theory of arithmetic, you should read Kreisel's Survey.

Proof theory of propositional logic Classical propositional logic, also called sentential logic, deals with sentences and propositions as abstract units which take on distinct True/False values.

The basic syntactic units of propositional A Proof Theory for Description Logics book arevariableswhich represent atomic propo- sitions which may have value eitherTrueorFalse.

We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic.

Now that we have speciﬁed a language of set theory, we could specify a proof system. We will not do this here—see n diﬀerent logic books for n diﬀerent proof systems.

However, these are essentially all the same— satisfying the completeness theorem (due to K. G¨odel) which essentially says. "An Introduction to Proof Theory". in Handbook of Proof Theory, edited by S. Buss. Elsevier, Amsterdam,pp Download article: postscript or PDF. Table of contents: This is an A Proof Theory for Description Logics book to proof complexity.

Proof theory and Propositional Logic. Frege proof systems. The propositional sequent calculus. Such Preferential Default Description Logics adhere to the principle of exception minimization and are therefore suited for certain tasks in Natural Language Processing.

A sound and complete proof theory is given, based on establishing a correspondence between models Author: Sven Suska. This book is meant to provide a thorough introduction to Description Logics, covering all the above-mentioned aspects of DL research—namely theory, imple- mentation, and applications.

The papers address the entire spectrum of research in automated reasoning including formalization of mathematics, proof theory, proof search, description logics, interactive proof checking, higher-order logic, combination methods, satisfiability procedures, and rewriting.

Aristotle's Syllogistic: From the Standpoint of Modern Logic by J. Lukasiewicz; Polish Logic Edited by Stors McCall; Prior's book has sections on propositional calculus, quantification theory, the Aristotelian syllogistic, traditional logic, modal logic, three-valued logic, and the logic of extension.

• Description logics can be understood from a modal logic perspective. • Each pair of 8R and 9R statements give rise to a pair of modalities.

• Essentially, some description logics are multi-modal logics. • See e.g. Baader et al., The Description Logic Handbook, Cambridge University Press, ( views) A Friendly Introduction to Mathematical Logic by Christopher C. Leary, Lars Kristiansen - Milne Library Publishing, In this book, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory.

the rest of the book. Divisibility is an extremely fundamental concept in number theory, and has applications including puzzles, encrypting messages, computer se-curity, and many algorithms.

An example is checking whether Universal Product Codes (UPC) or International Standard Book Number (ISBN) codes are Size: KB. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system.

As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Such Preferential Default Description Logics adhere to the principle of exception minimization and are therefore suited for certain tasks in Natural Language Processing.

A sound and complete proof theory is given, based on establishing a correspondence between models. Knowledge representation in Description Logics 16 From theory to practice: Description Logics systems 20 Applications developed with Description Logics systems 24 Extensions of Description Logics 34 Relationship to other ﬁelds of Computer Science 40 Conclusion 43 Part one: Theory 45 2 Basic Description Logics F.

Baader File Size: 4MB. To provide a thorough, concise introduction to Description Logics, covering the central topics and techniques of the ﬁeld, namely theory and implementation, whilst sketching their use in applications.

Target Audience The book will be suitable as a basis for a graduate (or advanced undergraduate)File Size: 64KB. Good Wool Traceable premium merino wool in fresh colors and silhouettes. Responsibly made and precisely tailored, this is workwear for the 21st century.

Water used in the dyeing and finishing of Good Wool is purified and returned to its source. Learn More. Women's Good Wool. Men's Good Wool. Good Wool is woven from traceable premium merino wool. Quick links. Teach Yourself Logic A Study Guide (find it on by preference, or here); Appendix: Some Big Books on Mathematical Logic (pdf); Book Notes (links to 37 book-by-book webpages, the content overlapping with the Appendix); In more detail, on TYL.

Most philosophy departments, and many maths departments too, teach little or no serious logic, despite the centrality. Full online text of the book.

Includes tutorial on Martin-Löf's type theory, motivating remarks on intuitionism, as well as sample formalisations of constructive mathematics in the NuPrl theorem prover. Petr K remen @ Introduction, Description Logics October 5, 13 / Logics for Ontologies propositional logic Example \John is clever):\John fails at exam rst order predicate logic Proof Theory { to enforce the semantics Logics trade-o A logical calculus is always a trade-o between expressiveness and.

Model and Proof Theory of Constructive ALC Constructive Description Logics. Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg Description logics (DLs) form a family of knowledge representation formalisms toAuthor: Stephan Scheele.

On The Proof Theory of ALC. This paper presents a version of Intuitionistic Description Logic designed for legal knowledge representation. The paper discusses a logical coherence analysis of.

Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems.

That’s the main book-measurement treatment of hybrid logic and its proof-precept. Hybrid logic is an extension of strange modal logic which allows particular reference to specific individual elements in a model (the place the elements characterize events, potential worlds, states in a.

There is now a large variety of approaches to proof theory for relevant logics. There is a sequent calculus for the negation-free fragment of the logic R due to Gregory Mints () and J.M. Dunn () and an elegant and very general approach called “Display Logic” developed by Nuel Belnap ().

For the former, see the supplementary. proof/explanation, with a performance reasoner already available for the language. 2 Description Logics Description Logics form a family of formalisms for repre senting and reasoning with knowledge, surveyed, among others, in [8; 16; 2].

The three fundamental notions of DLs are individuals, representing objects in the domain. In Studies in Logic and the Foundations of Mathematics, PROOF. Suppose that P is a cut-free proof of a constant-free sequent Γ ⇒ α with nonempty Γ By subformula property, P is a constant-free proof.A sequent Σ ⇒ δ in P is good if it contains at least two formulas, i.e., either both Σ and δ are nonempty, or δ is empty but Σ contains at least two formulas.

Tableau, Gentzen, and natural deduction style proof-theory for hybrid logic work very well compared to ordinary modal logic. Usually, when a modal tableau, Gentzen, or natural deduction system is given, it is for one particular modal logic and it has turned out to be problematic to formulate such systems for modal logics in a uniform way.

If you have a basic introduction to logic (e.g. Enderton's book or the book by Boolos, Burgess, and Jeffrey), you have the background to learn significant amounts of each of the four areas.

One thing most general introductions to logic lack is a solid background in basic set theory. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We introduce a new proof system for the description logic ALC in the framework of the calculus of structures, a structural proof theory that employs deep inference.

This new formal presentation introduces positive proofs for description logics. Moreover, this result makes possible the study of sub-structural. The modal logic perspective • Description logics can be understood from a modal logic perspective.

• Each pair of ∀ R and ∃ R statements give rise to a pair of modalities. • Essentially, some description logics are multi-modal logics. • See e.g. Baader et al., The Description Logic Handbook, Cambridge University Press, Description logics are embodied in several knowledge-based systems and are used to develop various real-life applications.

Now in paperback, The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely: theory, implementation, and applications/5.

in the lightweight description logics DL-Lite and ELH. The proof exploits known pdf of query matches in these logics and involves a query-dependent modiﬁcation of the data. To obtain a more practical approach, we propose a concrete polynomial-time algorithm for answering acyclic CQs based on rewriting queries into datalog pro-grams.A First Course in Logic book.

Read reviews from world’s largest community for readers. The ability to reason and think in a logical manner forms the basi /5(17).Probabilistic Description Logics. Semantic Web Incompleteness or uncertainty are intrinsic of much information ebook the World Wide Web Most common approaches: probability theory, Fuzzy Logic Probabilistic extensions of DL based on Bayesian networks [Koller et al.,Ding and Peng, ] Statistical terminological knowledge in PCL[Jaeger, ]File Size: 3MB.