- Computational Logic, Data and Knowledge Modeling, Relational Database, Formal methods, Games (Computer Science), Theoretical Computer Science, and 22 moreAutomata Theory (Formal Languages), Mathematical Logic, Logic, Databases (Relational, XML), Information Exchange, Lambda Calculus, Logical Methods in Computer Science, Databases, Computational Complexity, Finite Automata, Finite Model Theory, Caucal hierarchy, Counting Quantifiers, Monadic Second-Order Logic, Generalized Quantifier Theory, Boolean Conjunctive Queries, DESCRIPTIVE COMPLEXITY THEORY, Visibly Pushdown Automata, Query Answering, Morphic Words, and Finite Controllabilityedit
- student of logicedit
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Research Interests: Mathematics, Computer Science, Computational Complexity, Pure Mathematics, Databases, and 15 moreDiscrete Mathematics, Computer Software, Finite Model Theory, Logical Methods in Computer Science, Bisimulation, Boolean Conjunctive Queries, Description Logic, First Order Logic, Guarded Fragment, DESCRIPTIVE COMPLEXITY THEORY, Query Answering, Finite Controllability, Decidability, P, and Polynomial Time
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The finite satisfiability problem for guarded fixpoint logic is decidable and complete for 2ExpTime (resp. ExpTime for formulas of bounded width).
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Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic.... more
Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may not be guarded, well known results about the decidability, complexity, and finite-model property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati's finite chase, we prove for guarded theories F and (unions of) conjunctive queries Q that (i) Q is true in each model of F iff Q is true in each finite model of F and (ii) determining whether F implies Q is 2EXPTIME-complete. We further show the following results: (iii) the existence of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof of the fin...
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We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for... more
We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at most k is decidable; and that XPath is undecidable on any class of documents with unbounded braid width. We conjecture that these two parameters are equivalent, in the sense that a class of documents has bounded match width iff it has bounded braid width.
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Probabilistic programming languages are used for developing statistical models. They typically consist of two components: a specification of a stochastic process (the prior) and a specification of observations that restrict the... more
Probabilistic programming languages are used for developing statistical models. They typically consist of two components: a specification of a stochastic process (the prior) and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. In this article, we establish a probabilistic-programming extension of Datalog that, on the one hand, allows for defining a rich family of statistical models, and on the other hand retains the fundamental properties of declarativity. Our proposed extension provides mechanisms to include common numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by mean...
Research Interests:
We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectively the decidability of the MSO theory of... more
We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectively the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is canonical in a certain sense. We then go on to generalize our techniques to a hierarchy of classes of infinite words enjoying the above mentioned properties. We introduce k-lexicographic presentations, and morphisms of level k stacks and show that these are inter-translatable, thus giving rise to the same classes of k-lexicographic or level k morphic words. We prove that these presentations are also canonical, which implies decidability of the MSO theory of every k-lexicographic word as well as closure of these classes under restricted MSO interpretations, e.g. closure under deterministic sequential mappings. The classes of k-lexicographic wor...
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Automatic structures are countable structures finitely presentable by a collection of automata. We study questions related to properties invariant with respect to the choice of an automatic presentation. We give a
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Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is... more
Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdown language is a regular restriction of the set of well-matched words, meaning that the language can be accepted by a finite automaton if only well-matched words are considered as input.
We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSOinterpretability in algebraic trees, and the... more
We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSOinterpretability in algebraic trees, and the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is in a certain sense canonical. We then generalize our techniques to a hierarchy of classes of ω-words enjoying the above mentioned definability and decidability properties. We introduce k-lexicographic presentations, and morphisms of level k stacks and show that these are inter-translatable, thus giving rise to the same classes of k-lexicographic or level k morphic words. We prove that these presentations are also canonical, which implies decidability of the MSO theory of every k-lexicographic word as well as closure of these classes under MSO-definable recolorings, e.g. closure under deterministic sequential mapping...
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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
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The work at hand studies the possibilities and limitations of the use of finite automata in the description of infinite structures. An automatic presentation of a countable structure consists of a labelling of the elements of the... more
The work at hand studies the possibilities and limitations of the use of finite automata in the description of infinite structures. An automatic presentation of a countable structure consists of a labelling of the elements of the structure by finite words over a finite alphabet in a consistent way so as to allow each of the relations of the structure to be recognised, given the labelling, by a synchronous multi-tape automaton. The collection of automata involved constitutes a finite presentation of the structure up to isomorphism. More generally, one can consider presentations over finite trees or over infinite words or trees, based on the appropriate model of automata. In the latter models, uncountable structures are also representable. Automatic presentations allow for effective evaluation of first-order formulas over the represented structure in line with the strong correspondence between automata and logics. Accordingly, automatic presentations can be recast in logical terms
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We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend... more
We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic. We show that the satisfiability problem for GNFO and for GNFP is 2ExpTimecomplete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation.
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The model theory of finite structures is intimately connected to various fields
We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain... more
We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. By the standard correspondence between monadic second-order logic and automata, this shows that the extension of first-order logic by cardinality quantifiers collapses to pure first-order logic over injectively presentable ω-tree-automatic structures, which generalizes previous results by Kuske and Lohrey. Additionally, it follows from our proofs that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable since not all of these classes are analytic. Our method to eliminate the uncountability quantifier is based on Shelah’s composition method and basic results from descriptive set theory. It is constructive, yielding a decision pro...
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Abstract. Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it... more
Abstract. Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdown language is a regular restriction of the set of well-matched words, meaning that the language can be accepted by a finite automaton if only well-matched words are considered as input. 1
Research Interests:
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical... more
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guar...
We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSOinterpretability in algebraic trees, and the... more
We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSOinterpretability in algebraic trees, and the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is in a certain sense canonical. We then generalize our techniques to a hierarchy of classes of ω-words enjoying the above mentioned definability and decidability properties. We introduce k-lexicographic presentations, and morphisms of level k stacks and show that these are inter-translatable, thus giving rise to the same classes of k-lexicographic or level k morphic words. We prove that these presentations are also canonical, which implies decidability of the MSO theory of every k-lexicographic word as well as closure of these classes under MSO-definable recolorings, e.g. closure under deterministic sequential mapping...
Research Interests:
We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectively the decidability of the MSO theory of... more
We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectively the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is canonical in a certain sense. We then go on to generalize our techniques to a hierarchy of classes of infinite words enjoying the above mentioned properties. We introduce k-lexicographic presentations, and morphisms of level k stacks and show that these are inter-translatable, thus giving rise to the same classes of k-lexicographic or level k morphic words. We prove that these presentations are also canonical, which implies decidability of the MSO theory of every k-lexicographic word as well as closure of these classes under restricted MSO interpretations, e.g. closure under deterministic sequential mappings. The classes of k-lexicographic wor...
Research Interests:
Probabilistic programming languages are used for developing statistical models, and they typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the... more
Probabilistic programming languages are used for developing statistical models, and they typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. We propose and investigate an extension of Datalog for specifying statistical models, and establish a declarative probabilistic-programming paradigm over databases. Our proposed extension provides convenient mechanisms to include common numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by means of integrity constraints over the extensional and i...
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical... more
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guar...
Research Interests:
The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many... more
The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics.
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... known as the problem of query answering against a GFO theory, and it has been solved in [3 ... that without affecting satisfiability of (4) we may introduce new atoms guarding the existentialquantifiers in ψ ... We denote the... more
... known as the problem of query answering against a GFO theory, and it has been solved in [3 ... that without affecting satisfiability of (4) we may introduce new atoms guarding the existentialquantifiers in ψ ... We denote the predicates given by the relational schema by P, Q, R, S etc. ...
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We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets''. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain... more
We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets''. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic. Our approach is based on Shelah's composition method and uses basic results from descriptive set theory. The elimination result is constructive, yielding a decision procedure for the extended logic.
Research Interests:
We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets''. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain... more
We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets''. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic. Our approach is based on Shelah's composition method and uses basic results from descriptive set theory. The elimination result is constructive, yielding a decision procedure for the extended logic. Furthermore, by the well-known correspondence between monadic second-order logic and tree automata, our findings translate to analogous results on the extension of first-order logic by cardinality quantifiers over injectively presentable Rabin-automatic structures, generalizing the work of Kuske and Lohrey.
Research Interests:
Probabilistic programming languages are used for developing statistical models, and they typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the... more
Probabilistic programming languages are used for developing statistical models, and they typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. We propose and investigate an extension of Datalog for specifying statistical models, and establish a declarative probabilistic-programming paradigm over databases. Our proposed extension provides convenient mechanisms to include common numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. The resulting semantics is robust under different chases and invariant to rewritings that preserve logical equivalence.
Research Interests:
We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP,... more
We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are
required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called
GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic,
respectively. They also extend the recently introduced unary negation fragments of first-order logic and of
least fixpoint logic.
We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbi-
trary structures and on finite structures. We also study the complexity of the associated model checking
problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also
model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has
the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an
appropriate notion of bisimulation.
Our complexity upper bounds for GNFO and GNFP hold true even for their “clique-guarded” extensions
CGNFO and CGNFP, in which clique guards are allowed in the place of guards.
required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called
GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic,
respectively. They also extend the recently introduced unary negation fragments of first-order logic and of
least fixpoint logic.
We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbi-
trary structures and on finite structures. We also study the complexity of the associated model checking
problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also
model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has
the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an
appropriate notion of bisimulation.
Our complexity upper bounds for GNFO and GNFP hold true even for their “clique-guarded” extensions
CGNFO and CGNFP, in which clique guards are allowed in the place of guards.
Research Interests:
Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may... more
Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may not be guarded, well known results about the decidability, complexity, and finite-model property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati's finite chase, we prove for guarded theories F and (unions of) conjunctive queries Q that (i) Q is true in each model of F iff Q is true in each finite model of F and (ii) determining whether F implies Q is 2EXPTIME-complete. We further show the following results: (iii) the existence of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the clique-guarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomial-time solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded bisimulation invariant PTIME.
Research Interests:
"The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all unions of conjunctive queries, a restricted form of negation that suffices for expressing some common uses of negation in SQL queries, and a large... more
"The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all unions of conjunctive queries, a restricted form of negation that suffices for expressing some common uses of negation in SQL queries, and a large class of integrity constraints. At the same time, as was recently shown,
the syntax of GNFO is restrictive enough so that static analysis problems such as query containment are still decidable. This suggests that, in spite of its expressive power, GNFO queries are amenable to novel optimizations. In this paper we provide further evidence for this, establishing that GNFO queries have distinctive features with respect to rewriting. Our results include effective preservation theorems for GNFO, Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to GNFO constraints within very restricted logics."
the syntax of GNFO is restrictive enough so that static analysis problems such as query containment are still decidable. This suggests that, in spite of its expressive power, GNFO queries are amenable to novel optimizations. In this paper we provide further evidence for this, establishing that GNFO queries have distinctive features with respect to rewriting. Our results include effective preservation theorems for GNFO, Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to GNFO constraints within very restricted logics."
Research Interests:
We consider which queries are answerable in the presence of access restrictions and integrity constraints, and which portions of the schema are accessible in the presence of access restrictions and constraints. Unlike prior work, we focus... more
We consider which queries are answerable in the presence of access restrictions and integrity constraints, and which portions of the schema are accessible in the presence of access restrictions and constraints. Unlike prior work, we focus on integrity constraint languages that subsume inclusion dependencies. We also use a semantic de nition of answerability: a query is answerable if the accessible information is sucient to determine its truth value. We show that answerability is decidable for the class of guarded dependencies, which includes all inclusion dependencies, and also for constraints given in the guarded fragment of first-order
logic. We also show that answerable queries "have query plans" in a restricted language. We give corresponding results for extractability of portions of the schema. Our results relate querying with limited access patterns, determinacy-vs-rewriting, and analysis of guarded constraints.""
logic. We also show that answerable queries "have query plans" in a restricted language. We give corresponding results for extractability of portions of the schema. Our results relate querying with limited access patterns, determinacy-vs-rewriting, and analysis of guarded constraints.""
Research Interests:
We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for... more
We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at most k is decidable; and that XPath is undecidable on any class of documents with unbounded braid width. We conjecture that these two parameters are equivalent, in the sense that a class of documents has bounded match width iff it has bounded braid width.
Research Interests:
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical... more
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that most usage of negation in SQL in practice is guarded negation.
Research Interests:
"We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP,... more
"We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic.
We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-
complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation."
We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-
complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation."
Research Interests:
The finite satisfiability problem for guarded fixpoint logic is decidable and complete for 2ExpTime (resp. ExpTime for formulas of bounded width).
Research Interests:
Evaluating a boolean conjunctive query q over a guarded first-order theory T is equivalent to checking whether (T & not q) is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not... more
Evaluating a boolean conjunctive query q over a guarded first-order theory T is equivalent to checking whether (T & not q) is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity, and finite-model property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati’s finite chase, we prove for guarded theories T and (unions of) conjunctive queries q that (i) T implies q iff T implies q over finite models, that is, iff q is true in each finite model of T and (ii) determining whether T implies q is 2EXPTIME-complete. We further show the following results: (iii) the existence of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the clique-guarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomial-time solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded-bisimulation-invariant PTIME.
Research Interests:
"We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain... more
"We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order.
Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic.
Our approach is based on Shelah’s composition method and uses basic results from descriptive set theory. The elimination result is constructive, yielding a decision procedure for the extended logic."
Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic.
Our approach is based on Shelah’s composition method and uses basic results from descriptive set theory. The elimination result is constructive, yielding a decision procedure for the extended logic."
Research Interests:
"We study the extension of monadic second-order logic of order with cardinality quantifiers “there exists infinitely many sets” and “there exists uncountably many sets”. On linear orders that require the addition of only countably many... more
"We study the extension of monadic second-order logic of order with cardinality quantifiers “there exists infinitely many sets” and “there exists uncountably many sets”. On linear orders that require the addition of only countably many points to be complete, we show using the composition method that the second-order uncountability quantifier can be reduced to the first-order uncountability quantifier. In particular, this shows that the extension of monadic second-order logic with this quantifier has the same expressive power as monadic second-order logic over ordinals and over countable scattered linear orders. Using a Ramsey-like theorem of Shelah for dense linear orders we show how to eliminate the uncountability quantifier over the ordering of the rationals. Hence, ultimately, we give an elimination procedure that works over all countable linear orders.
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