Michael Zakharyaschev

Bio: Michael Zakharyaschev is an academic researcher from Birkbeck, University of London. The author has contributed to research in topics: Description logic & Decidability. The author has an hindex of 48, co-authored 246 publications receiving 10169 citations. Previous affiliations of Michael Zakharyaschev include University of Bremen & National Research University – Higher School of Economics.

Monodic fragments of first-order temporal logics: 2000-2001 A.D

Abstract: The aim of this paper is to summarize and analyze some results obtained in 2000-2001 about decidable and undecidable fragments of various first-order temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the 'temporal community' to a number of interesting open problems.

Semi-qualitative Reasoning about Distances: A Preliminary Report

Abstract: We introduce a family of languages intended for representing knowledge and reasoning about metric (and more general distance) spaces. While the simplest language can speak only about distances between individual objects and Boolean relations between sets, the more expressive ones are capable of capturing notions such as 'somewhere in (or somewhere out of) the sphere of a certain radius', 'everywhere in a certain ring', etc. The computational complexity of the satisfiability problem for formulas in our languages ranges from NP-completeness to undecidability and depends on the class of distance spaces in which they are interpreted. Besides the class of all metric spaces, we consider, for example, the spaces R × R and N × N with their natural metrics.

Many-Dimensional Modal Logics: Theory and Applications

Abstract: I Introduction 1 Modal logic basics 1.1 Modal axiomatic systems 1.2 Possible world semantics 1.3 Classical first-order logic and the standard translation 1.4 Multimodal logics 1.5 Algebraic semantics 1.6 Decision, complexity and axiomatizability problems 2 Applied modal logic 2.1 Temporal logic 2.2 Interval temporal logic 2.3 Epistemic logic 2.4 Dynamic logic 2.5 Description logic 2.6 Spatial logic 2.7 Intuitionistic logic 2.8 'Model level' reductions between logics 3 Many-dimensional modal logics 3.1 Fusions 3.2 Spatio-temporal logics 3.3 Products 3.4 Temporal epistemic logics 3.5 Classical first-order logic as a propositional multimodal logic 3.6 First-order modal logics 3.7 First-order temporal logics 3.8 Description logics with modal operators 3.9 HS as a two-dimensional logic 3.10 Modal transition logics 3.11 Intuitionistic modal logics II Fusions and products 4 Fusions of modal logics 4.1 Preserving Kripke completeness and the finite model property 4.2 Algebraic preliminaries 4.3 Preserving decidability of global consequence 4.4 Preserving decidability 4.5 Preserving interpolation 4.6 On the computational complexity of fusions 5 Products of modal logics: introduction 5.1 Axiomatizing products 5.2 Proving decidability with quasimodels 5.3 The finite model property 5.4 Proving undecidability 5.5 Proving complexity with tilings 6 Decidable products 6.1 Warming up: Kn x Km 6.2 CPDL x K_m 6.3 Products of epistemic logics with Km 6.4 Products of temporal logics with Km 6.5 Products with S5 6.6 Products with multimodal S5 7 Undecidable products 7.1 Products of linear orders with infinite ascending chains 7.2 Products of linear orders with infinite descending chains 7.3 Products of Dedekind complete linear orders 7.4 Products of finite linear orders 7.5 More undecidable products 8 Higher-dimensional products 8.1 S5 x S5 x ... x S5 8.2 Products between K4 x K4 x ... x K4 and S5 x S5 x ... x S5 8.3 Products with the fmp 8.4 Between K x K x ... x K and S5 x S5 x ... x S5 8.5 Finitely axiomatizable and decidable products 9 Variations on products 9.1 Relativized products 9.2 Valuation restrictions 10 Intuitionistic modal logics 10.1 Intuitionistic modal logics with Box 10.2 Intuitionistic modal logics with Box and Diamond 10.3 The finite model property III First-order modal logics 11 Fragments of first-order temporal logics 11.1 Undecidable fragments 11.2 Monodic formulas, decidable fragments 11.3 Embedding into monadic second-order theories 11.4 Complexity of decidable fragments of QLogSU(N) 11.5 Satisfiability in models over (N,<) with finite domains 11.6 Satisfiability in models over (R,<) with finite domains 11.7 Axiomatizing monodic fragments 11.8 Monodicity and equality 12 Fragments of first-order dynamic and epistemic logics 12.1 Decision problems 12.2 Axiomatizing monodic fragments IV Applications to knowledge representation 13 Temporal epistemic logics 13.1 Synchronous systems 13.2 Agents who know the time and neither forget nor learn 14 Modal description logics 14.1 Concept satisfiability 14.2 General formula satisfiability 14.3 Restricted formula satisfiability 14.4 Satisfiability in models with finite domains 15 Tableaux for modal description logics 15.1 Tableaux for ALC 15.2 Tableaux for K(ALC) with constant domains 15.3 Adding expressive power to K(ALC) 16 Spatio-temporal logics 16.1 Modal formalisms for spatio-temporal reasoning 16.2 Embedding spatio-temporal logics in first-order temporal logic 16.3 Complexity of spatio-temporal logics 16.4 Models based on Euclidean spaces Epilogue. Bibliography. List of tables. List of languages and logics. Symbol index. Subject index.

The DL-lite family and relations

Abstract: The recently introduced series of description logics under the common moniker 'DL-Lite' has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and the ability to represent conceptual modeling formalisms, on the other. The main aim of this article is to carry out a thorough and systematic investigation of inference in extensions of the original DL-Lite logics along five axes: by (i) adding the Boolean connectives and (ii) number restrictions to concept constructs, (iii) allowing role hierarchies, (iv) allowing role disjointness, symmetry, asymmetry, reflexivity, irreflexivity and transitivity constraints, and (v) adopting or dropping the unique name assumption. We analyze the combined complexity of satisfiability for the resulting logics, as well as the data complexity of instance checking and answering positive existential queries. Our approach is based on embedding DL-Lite logics in suitable fragments of the one-variable first-order logic, which provides useful insights into their properties and, in particular, computational behavior.

A Temporal Logic of Nested Calls and Returns

Abstract: Model checking of linear temporal logic (LTL) specifications with respect to pushdown systems has been shown to be a useful tool for analysis of programs with potentially recursive procedures. LTL, however, can specify only regular properties, and properties such as correctness of procedures with respect to pre and post conditions, that require matching of calls and returns, are not regular. We introduce a temporal logic of calls and returns (CaRet) for specification and algorithmic verification of correctness requirements of structured programs. The formulas of CaRet are interpreted over sequences of propositional valuations tagged with special symbols call and ret. Besides the standard global temporal modalities, CaRet admits the abstract-next operator that allows a path to jump from a call to the matching return. This operator can be used to specify a variety of non-regular properties such as partial and total correctness of program blocks with respect to pre and post conditions. The abstract versions of the other temporal modalities can be used to specify regular properties of local paths within a procedure that skip over calls to other procedures. CaRet also admits the caller modality that jumps to the most recent pending call, and such caller modalities allow specification of a variety of security properties that involve inspection of the call-stack. Even though verifying context-free properties of pushdown systems is undecidable, we show that model checking CaRet formulas against a pushdown model is decidable. We present a tableau construction that reduces our model checking problem to the emptiness problem for a Buchi pushdown system. The complexity of model checking CaRet formulas is the same as that of checking LTL formulas, namely, polynomial in the model and singly exponential in the size of the specification.

Ontology Matching

Abstract: Ontologies tend to be found everywhere. They are viewed as the silver bullet for many applications, such as database integration, peer-to-peer systems, e-commerce, semantic web services, or social networks. However, in open or evolving systems, such as the semantic web, different parties would, in general, adopt different ontologies. Thus, merely using ontologies, like using XML, does not reduce heterogeneity: it just raises heterogeneity problems to a higher level. Euzenat and Shvaikos book is devoted to ontology matching as a solution to the semantic heterogeneity problem faced by computer systems. Ontology matching aims at finding correspondences between semantically related entities of different ontologies. These correspondences may stand for equivalence as well as other relations, such as consequence, subsumption, or disjointness, between ontology entities. Many different matching solutions have been proposed so far from various viewpoints, e.g., databases, information systems, and artificial intelligence. The second edition of Ontology Matching has been thoroughly revised and updated to reflect the most recent advances in this quickly developing area, which resulted in more than 150 pages of new content. In particular, the book includes a new chapter dedicated to the methodology for performing ontology matching. It also covers emerging topics, such as data interlinking, ontology partitioning and pruning, context-based matching, matcher tuning, alignment debugging, and user involvement in matching, to mention a few. More than 100 state-of-the-art matching systems and frameworks were reviewed. With Ontology Matching, researchers and practitioners will find a reference book that presents currently available work in a uniform framework. In particular, the work and the techniques presented in this book can be equally applied to database schema matching, catalog integration, XML schema matching and other related problems. The objectives of the book include presenting (i) the state of the art and (ii) the latest research results in ontology matching by providing a systematic and detailed account of matching techniques and matching systems from theoretical, practical and application perspectives.

The Description Logic Handbook

Abstract: This introduction presents the main motivations for the development of Description Logics (DLs) as a formalism for representing knowledge, as well as some important basic notions underlying all systems that have been created in the DL tradition. In addition, we provide the reader with an overview of the entire book and some guidelines for reading it. We first address the relationship between Description Logics and earlier semantic network and frame systems, which represent the original heritage of the field. We delve into some of the key problems encountered with the older efforts. Subsequently, we introduce the basic features of DL languages and related reasoning techniques. DL languages are then viewed as the core of knowledge representation systems, considering both the structure of a DL knowledge base and its associated reasoning services. The development of some implemented knowledge representation systems based on Description Logics and the first applications built with such systems are then reviewed. Finally, we address the relationship of Description Logics to other fields of Computer Science.We also discuss some extensions of the basic representation language machinery; these include features proposed for incorporation in the formalism that originally arose in implemented systems, and features proposed to cope with the needs of certain application domains.