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An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic

Sven Hartmann, Sebastian Link
2006 Electronical Notes in Theoretical Computer Science  
We extend the result on the equivalence between functional and multivalued dependencies in relational databases and a fragment of propositional logic.  ...  It is well-known that the implication of FDs and MVDs is equivalent to the logical implication of formulae in a certain fragment of propositional logic [21] .  ...  It remains to demonstrate the equivalence between 2) and 3). First, we show that 2) implies 3). Suppose Π ∪ Π N does not logically imply Φ(σ).  ... 
doi:10.1016/j.entcs.2005.04.039 fatcat:eyrkx6krebdbhomzszf2h74g2m

Characterising nested database dependencies by fragments of propositional logic

Sven Hartmann, Sebastian Link
2008 Annals of Pure and Applied Logic  
We extend the earlier results on the equivalence between the Boolean and the multivalued dependencies in relational databases and fragments of the Boolean propositional logic.  ...  Secondly, they characterise the implication of data dependencies in nested databases in purely logical terms.  ...  Acknowledgement This research is supported by the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand.  ... 
doi:10.1016/j.apal.2007.11.004 fatcat:tanr2vwpjna5lodvkpqawlejdu

A unified approach to structured and XML data modeling and manipulation

Matteo Magnani, Danilo Montesi
2006 Data & Knowledge Engineering  
In this paper we propose an approach to defining logical database models, based on the instantiation of a general abstract model, and discuss its application to the management of mixed XML/relational data  ...  We present an instantiation of our model that unifies the main approaches to represent and manipulate relational and XML data, and in particular SQL, SQL/XML, XQuery, and Oracle's XML Type.  ...  The logical level provides an abstract representation of databases.  ... 
doi:10.1016/j.datak.2005.06.004 fatcat:zgjksx53jfhkbawr7t3ungyvom

Fixed-Point Logics and Solitaire Games

Dietmar Berwanger, Erich Gr�del
2004 Theory of Computing Systems  
We study Solitaire-LFP, a fragment of least fixedpoint logic, whose evaluation games are nested soltaire games.  ...  On finite structures (but not on infinite ones), Solitaire-LFP is equivalent to transitive closure logic. We also consider the solitaire fragment of guarded fixed-point logics.  ...  A corresponding fragment of the modal µ-calculus has already been studied in [8] , and has been shown to be equivalent to the logic ECTL * .  ... 
doi:10.1007/s00224-004-1147-5 fatcat:o7bj3ruwkzgxxdqqnsdcboehpm

Three-Valued Logics, Uncertainty Management and Rough Sets [chapter]

Davide Ciucci, Didier Dubois
2014 Lecture Notes in Computer Science  
This paper is a survey of the connections between threevalued logics and rough sets from the point of view of incomplete information management.  ...  equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets.  ...  A rough set, viewed as a pair of nested approximations is a typical example of ill-known set, where the lack of knowledge comes from an equivalence relation between possibly indistinguishable elements,  ... 
doi:10.1007/978-3-642-54756-0_1 fatcat:o7vun6jnzncxrizq3vfwxvji34

On the relation between possibilistic logic and modal logics of belief and knowledge

Mohua Banerjee, Didier Dubois, Lluis Godo, Henri Prade
2017 Journal of Applied Non-Classical Logics  
Generalized possibilistic logic (GPL) extends both possibilistic logic and MEL, and has a semantics in terms of sets of possibility distributions.  ...  On the other hand, in the so-called meta-epistemic logic (MEL) an agent can express both all-or-nothing beliefs and explicitly ignored facts, by only using modal formulas of depth 1, and no objective ones  ...  MEL + and MEL ++ are respectively equivalent to the non-nested fragments of modal systems KD45 and S5.  ... 
doi:10.1080/11663081.2018.1439357 fatcat:s3ejaqjk6jhqdoxqytkm2npbim

How Can Reasoners Simplify Database Querying (And Why Haven't They Done It Yet)?

Michael Benedikt
2018 Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - SIGMOD/PODS '18  
We undertake a review of some of the results and reasoning algorithms that have been developed with a motivation from query evaluation, and add to this a look at open problems in the area as well as a  ...  The purpose of this article is to reflect on the use of reasoning for rewriting and simplifying relational database queries.  ...  The research was supported by EPSRC grants EP/M005852/1, EP/N014359/1, and EP/L012138/1.  ... 
doi:10.1145/3196959.3196989 dblp:conf/pods/Benedikt18 fatcat:fmx4gidgbzb6fpxtvrsy4eyskm

Propositional Reasoning about Saturated Conditional Probabilistic Independence [chapter]

Sebastian Link
2012 Lecture Notes in Computer Science  
The equivalence extends the duality between the propositional fragment and multivalued dependencies in relational databases to a trinity involving saturated conditional independencies.  ...  Special probability models allow us to establish a semantic proof for the equivalence between the implication of saturated conditional independencies and formulae in a Boolean propositional fragment.  ...  This research is supported by the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand.  ... 
doi:10.1007/978-3-642-32621-9_19 fatcat:6guu6v3g2nbife6txjprjodpau

XPath, transitive closure logic, and nested tree walking automata

Balder ten Cate, Luc Segoufin
2008 Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '08  
Balder ten Cate ISLA, Universiteit van Amsterdam and Luc Segoufin INRIA, ENS-Cachan We study FO(MTC), first-order logic with monadic transitive closure, a logical formalism in between FO and MSO on trees  ...  We also present a temporal logic on trees that is expressively complete for FO(MTC), in the form of an extension of the XML document navigation language XPath with two operators: the Kleene star for taking  ...  The extension to arbitrary is a bit tricky: A relative behavior of a -nested TWA in depends on the behavior of ( − 1)-nested TWA in , but this depends on the relative behaviors of ( − 2)-nested TWA in  ... 
doi:10.1145/1376916.1376952 dblp:conf/pods/CateS08 fatcat:wymzhsa76zc5bpkuyta2leno2e

Page 3634 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
N-Prolog is an extension of Prolog proposed by Gabbay and Reyle (1984, 1985) which allows for occurrences of nested implications in both goals and clauses.  ...  More exactly, we introduce a natural modal three-valued logic PK and we prove that a goal is derivable from a propositional program if and only if it is implied by the completion of the problem in the  ... 

Querying graph databases with XPath

Leonid Libkin, Wim Martens, Domagoj Vrgoč
2013 Proceedings of the 16th International Conference on Database Theory - ICDT '13  
., first-order logic), and the low complexity of query evaluation for many fragments.  ...  This further confirms the usefulness of XPath for graph querying. Full GXPath reg is more expressive and corresponds to a fragment of the transitive closure logic.  ...  This work was supported by the FET-Open project FoX (Foundations of XML), grant agreement FP7-ICT-233599, by EPSRC grant G049165, and by DFG grant MA 4938/2-1.  ... 
doi:10.1145/2448496.2448513 dblp:conf/icdt/LibkinMV13 fatcat:i34u6ty3afh3na3yay6s3ab76a

On temporal logic versus datalog

Irène Guessarian, Eugénie Foustoucos, Theodore Andronikos, Foto Afrati
2003 Theoretical Computer Science  
We provide a direct and modular translation from the temporal logics CTL, ETL, FCTL (CTL extended with the ability to express fairness) and the Modal -calculus to Monadic inf-Datalog with built-in predicates  ...  We characterize the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal -calculus and Modal -calculus).  ...  =or suggestions and the anonymous referees for insightful reading and helpful comments which greatly helped in improving the paper.  ... 
doi:10.1016/s0304-3975(02)00447-4 fatcat:dk2jtxhk2vgi7g22gjqgrc5fn4

Boolean Dependence Logic and Partially-Ordered Connectives [article]

Johannes Ebbing, Lauri Hella, Peter Lohmann, Jonni Virtema
2014 arXiv   pre-print
We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable.  ...  We define natural syntactic fragments of Boolean dependence logic and show that they coincide with the corresponding fragments of first-order logic enriched by partially-ordered connectives with respect  ...  The translations defined in Lemmas 3.5 and 3.6 directly yield the following equivalences between fragments of F O(POC) and F O(D) as well.  ... 
arXiv:1406.7132v1 fatcat:eo4kgizkene3pmuy4sqdi6w5rm

Efficient and Expressive Tree Filters [chapter]

Michael Benedikt, Alan Jeffrey
2007 Lecture Notes in Computer Science  
We deal with a logic equivalent to the XPath language, and also an extension with an Until operator.  ...  We further show that these fragments are expressively complete. Our results make use of techniques developed for the study of Linear Temporal Logic, applied to XML filtering.  ...  We will restrict our attention to un-nested documents; equivalently, we assume that our trees satisfy a "non-recursive DTD" -one in which the dependency relation between tags is acyclic.  ... 
doi:10.1007/978-3-540-77050-3_38 fatcat:lszb6sjx7zajdkvmvcnambhlg4

Boolean Dependence Logic and Partially-Ordered Connectives [chapter]

Johannes Ebbing, Lauri Hella, Peter Lohmann, Jonni Virtema
2013 Lecture Notes in Computer Science  
We introduce a new variant of dependence logic (D) called Boolean dependence logic (BD). In BD dependence atoms are of the type =(x 1 , . . . , x n , α), where α is a Boolean variable.  ...  We define natural syntactic fragments of BD and show that they coincide with the corresponding fragments of F O(POC) with respect to expressive power.  ...  The translations defined in Lemmas 3.5 and 3.6 directly yield the following equivalences between fragments of F O(POC) and F O(D) as well.  ... 
doi:10.1007/978-3-642-39992-3_12 fatcat:shnqfyssljarffvliov6zvm6aa
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