Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees.

[1]  Joachim Niehren,et al.  Feature Automata and Recognizable Sets of Feature Trees , 1993, TAPSOFT.

[2]  Georg Gottlob,et al.  Conjunctive queries over trees , 2004, JACM.

[3]  James W. Thatcher,et al.  Characterizing Derivation Trees of Context-Free Grammars through a Generalization of Finite Automata Theory , 1967, J. Comput. Syst. Sci..

[4]  Radu Mateescu,et al.  Local Model-Checking of Modal Mu-Calculus on Acyclic Labeled Transition Systems , 2002, TACAS.

[5]  Wolfgang Thomas,et al.  Languages, Automata, and Logic , 1997, Handbook of Formal Languages.

[6]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs V: On Closing the Gap Between Definability and Recognizability , 1991, Theor. Comput. Sci..

[7]  Luca Cardelli,et al.  Anytime, anywhere: modal logics for mobile ambients , 2000, POPL '00.

[8]  John Doner,et al.  Tree Acceptors and Some of Their Applications , 1970, J. Comput. Syst. Sci..

[9]  Thomas Schwentick,et al.  Expressive and efficient pattern languages for tree-structured data (extended abstract) , 2000, PODS '00.

[10]  Christoph Koch,et al.  Query evaluation on compressed trees , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[11]  Frank Neven.  Design and analysis of query languages for structured documents. A formal and logical approach , 1999 .

[12]  Georg Gottlob,et al.  The complexity of acyclic conjunctive queries , 2001, JACM.

[13]  Zoltán Ésik,et al.  On Logically Defined Recognizable Tree Languages , 2003, FSTTCS.

[14]  J. Büchi.  Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[15]  Thomas Schwentick,et al.  When is the evaluation of conjunctive queries tractable? , 2001, STOC '01.

[16]  Thomas Schwentick,et al.  Query automata over finite trees , 2002, Theor. Comput. Sci..

[17]  Leonid Libkin,et al.  Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series) , 2004 .

[18]  Joachim Niehren,et al.  Tree Automata , 2005 .

[19]  Pablo Barceló,et al.  Temporal logics over unranked trees , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[20]  Michael Benedikt,et al.  Regular Tree Languages Definable in FO , 2005, STACS.

[21]  K. N. Venkataraman,et al.  Decidability of the purely existential fragment of the theory of term algebras , 1987, JACM.

[22]  Thomas Schwentick,et al.  Numerical document queries , 2003, PODS.

[23]  Igor Walukiewicz,et al.  Characterizing EF and EX tree logics , 2006, Theor. Comput. Sci..

[24]  Giacomo Lenzi,et al.  Relating levels of the mu-calculus hierarchy and levels of the monadic hierarchy , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[25]  Silvano Dal-Zilio,et al.  A logic you can count on , 2004, POPL.

[26]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[27]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[28]  Gert Smolka,et al.  Feature-Constraint Logics for Unification Grammars , 1989, J. Log. Program..

[29]  Thomas Schwentick,et al.  Finite state machines for strings over infinite alphabets , 2004, TOCL.

[30]  Jacques Sakarovitch,et al.  Synchronized Rational Relations of Finite and Infinite Words , 1993, Theor. Comput. Sci..

[31]  Maarten Marx,et al.  First Order Paths in Ordered Trees , 2005, ICDT.

[32]  Damian Niwinski,et al.  Fixed points vs. infinite generation , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[33]  Maarten Marx,et al.  Conditional XPath, the first order complete XPath dialect , 2004, PODS.

[34]  Joachim Niehren,et al.  The first-order theory of ordering constraints over feature trees , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[35]  Yannis Papakonstantinou,et al.  DTD inference for views of XML data , 2000, PODS.

[36]  E. Allen Emerson,et al.  Tree automata, mu-calculus and determinacy , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[37]  Holger Schlingloff.  Expressive completeness of temporal logic of trees , 1992, J. Appl. Non Class. Logics.

[38]  Frank Neven,et al.  Logical definability and query languages over unranked trees , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[39]  Robert T. Kasper,et al.  A Logical Semantics for Feature Structures , 1986, ACL.

[40]  Maarten Marx,et al.  Conditional XPath , 2005, TODS.

[41]  M. de Rijke,et al.  Semantic characterizations of navigational XPath , 2005, SGMD.

[42]  Wolfgang Thomas,et al.  Regular Tree Languages Without Unary Symbols are Star-Free , 1993, FCT.

[43]  Achim Blumensath,et al.  Automatic structures , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[44]  Nicole Schweikardt,et al.  Comparing the Succinctness of Monadic Query Languages over Finite Trees , 2003, CSL.

[45]  Joachim Niehren,et al.  Minimizing Tree Automata for Unranked Trees , 2005, DBPL.

[46]  Derick Wood,et al.  Regular tree and regular hedge languages over unranked alphabets , 2001 .

[47]  Thomas Schwentick,et al.  Towards Regular Languages over Infinite Alphabets , 2001, MFCS.

[48]  Georg Gottlob,et al.  The complexity of XPath query evaluation and XML typing , 2005, JACM.

[49]  Faron Moller,et al.  Counting on CTL*: on the expressive power of monadic path logic , 2003, Inf. Comput..

[50]  Joachim Niehren,et al.  Querying Unranked Trees with Stepwise Tree Automata , 2004, RTA.

[51]  Nicole Schweikardt,et al.  Tight lower bounds for query processing on streaming and external memory data , 2005, Theor. Comput. Sci..

[52]  Wolfgang Thomas,et al.  Computation Tree Logic CTL* and Path Quantifiers in the Monadic Theory of the Binary Tree , 1987, ICALP.

[53]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[54]  Steven J. DeRose,et al.  XML Path Language (XPath) , 1999 .

[55]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[56]  Igor Walukiewicz.  Monadic second-order logic on tree-like structures , 2002, Theor. Comput. Sci..

[57]  Howard Straubing.  Finite Automata, Formal Logic, and Circuit Complexity , 1994, Progress in Theoretical Computer Science.

[58]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs , 1990, Inf. Comput..

[59]  Thomas Schwentick.  On Diving in Trees , 2000, MFCS.

[60]  Patrick Blackburn.  Structures, Languages and Translations: the Structural Approach to Feature Logic , 1994 .

[61]  Alexander Moshe Rabinovich,et al.  Expressive Power of Temporal Logics , 2002, CONCUR.

[62]  Patricia Bouyer,et al.  An Algebraic Characterization of Data and Timed Languages , 2001, CONCUR.

[63]  Moshe Y. Vardi.  Reasoning about The Past with Two-Way Automata , 1998, ICALP.

[64]  Alain Quéré,et al.  Définition et Etude des Bilangages Réguliers , 1968, Inf. Control..

[65]  Victor Vianu,et al.  Validating streaming XML documents , 2002, PODS.

[66]  Jean-Marc Talbot,et al.  Expressiveness of spatial logic for trees , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[67]  Bob Carpenter,et al.  The logic of typed feature structures , 1992 .

[68]  Luca Cardelli,et al.  Describing semistructured data , 2001, SGMD.

[69]  Johan Anthory Willem Kamp,et al.  Tense logic and the theory of linear order , 1968 .

[70]  Thomas Schwentick,et al.  Two-variable logic on data trees and XML reasoning , 2009, JACM.

[71]  Thomas Schwentick,et al.  Definable relations and first-order query languages over strings , 2003, JACM.

[72]  James W. Thatcher,et al.  Generalized finite automata theory with an application to a decision problem of second-order logic , 1968, Mathematical systems theory.

[73]  Christoph Koch,et al.  On the complexity of nonrecursive XQuery and functional query languages on complex values , 2006, TODS.

[74]  A. Arnold,et al.  Rudiments of μ-calculus , 2001 .

[75]  Thomas Schwentick,et al.  Two-Variable Logic on Words with Data , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[76]  Luca Cardelli,et al.  A Query Language Based on the Ambient Logic , 2001, SEBD.

[77]  Marcus Fontoura,et al.  Buffering in query evaluation over XML streams , 2005, PODS '05.

[78]  Gabriel M. Kuper,et al.  Structural properties of XPath fragments , 2003, Theor. Comput. Sci..

[79]  Masako Takahashi,et al.  Generalizations of Regular Sets and Their Applicatin to a Study of Context-Free Languages , 1975, Inf. Control..

[80]  Helmut Seidl,et al.  Locating Matches of Tree Patterns in Forests , 1998, FSTTCS.

[81]  Luca Cardelli,et al.  Deciding validity in a spatial logic for trees , 2005, J. Funct. Program..

[82]  M. Rabin.  Decidability of second-order theories and automata on infinite trees. , 1969 .

[83]  Georg Gottlob,et al.  Monadic queries over tree-structured data , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[84]  Marcelo Arenas,et al.  Combining Temporal Logics for Querying XML Documents , 2007, ICDT.

[85]  Bill Keller.  Feature Logics, Infinitary Descriptions, and Grammar , 1993 .

[86]  Albert R. Meyer,et al.  Cosmological lower bound on the circuit complexity of a small problem in logic , 2002, JACM.

[87]  Martin Grohe,et al.  The complexity of first-order and monadic second-order logic revisited , 2004, Ann. Pure Appl. Log..

[88]  Frank Neven,et al.  Automata, Logic, and XML , 2002, CSL.

[89]  Dominique Perrin,et al.  Finite Automata , 1958, Philosophy.

[90]  Victor Vianu,et al.  A Web Odyssey: from Codd to XML , 2001, PODS.

[91]  Wolfgang Thomas.  On Chain Logic, Path Logic, and First-Order Logic over Infinite Trees , 1987, LICS.

[92]  Thomas Schwentick,et al.  Counting in Trees for Free , 2004, ICALP.