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PDL for ordered trees

Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Bertrand Gaiffe, Evan Goris, Maarten Marx, Maarten de Rijke
2005 Journal of Applied Non-Classical Logics  
This paper is about a special version of PDL, proposed by Marcus Kracht, for reasoning about sibling ordered trees.  ...  While we are still some way from definitive answers to these questions, we discuss two first-order fragments of the PDL language for ordered trees, and show how the language can be used to express some  ...  and Hans-Joerg Tiede for valuable feedback.  ... 
doi:10.3166/jancl.15.115-135 fatcat:xklqtycx4nad5eii66vdjtbqxe

Complexity of Subtype Satisfiability over Posets [chapter]

Joachim Niehren, Tim Priesnitz, Zhendong Su
2005 Lecture Notes in Computer Science  
We present a uniform treatment of different flavors of subtyping: simple versus recursive types and structural versus non-structural subtype orders.  ...  In this paper, we investigate algorithms for and the complexity of subtype satisfiability over general posets.  ...  PDL over finite unranked ordered trees were proposed for computational linguistics applications [5] and found recent interest for querying XML documents.  ... 
doi:10.1007/978-3-540-31987-0_25 fatcat:wuz2ulrolvdkfafrpdcr7jgece

Temporal Logics Beyond Regularity

Martin Lange
2007 BRICS Report Series  
In particular, it features Propositional Dynamic Logic of Context-Free Programs, Fixpoint Logic with Chop, the Modal Iteration Calculus, and Higher-Order Fixpoint Logic.  ...  FLC has tree model property no finite model property L.  ...  The Expressive Power of L µ Emerson,Jutla '91 Every L µ -definable property is a regular tree language. Janin,Walukiewicz '96 Every bisimulation-invariant regular tree language is L µ -definable.  ... 
doi:10.7146/brics.v14i13.22178 fatcat:s4wi6d5ewffnrpew3leughbmhm

Document Retrieval on Repetitive Collections [chapter]

Gonzalo Navarro, Simon J. Puglisi, Jouni Sirén
2014 Lecture Notes in Computer Science  
PDL [4] builds a sparse suffix tree for the collection, and stores the answers to document listing queries for the nodes of the tree.  ...  One interesting order is the top-k order: store the identifiers in the order they should be returned by a topk() query. This forms the basis of our new PDL structure for top-k document retrieval.  ... 
doi:10.1007/978-3-662-44777-2_60 fatcat:jhvibdkgxfgibfwtdqbyjsc764

Document Retrieval on Repetitive Collections [article]

Gonzalo Navarro, Simon J. Puglisi, Jouni Sirén
2014 arXiv   pre-print
PDL [4] builds a sparse suffix tree for the collection, and stores the answers to document listing queries for the nodes of the tree.  ...  One interesting order is the top-k order: store the identifiers in the order they should be returned by a topk() query. This forms the basis of our new PDL structure for top-k document retrieval.  ...  Only one core was used for the queries. The operating system was Ubuntu 12.04 with Linux kernel 3.2.0. For Enwiki, we used search terms from an MSN query log with stop words filtered out.  ... 
arXiv:1404.4909v2 fatcat:cn2rng2jrzd4tawh5xv2jfxsb4

Model-Checking Parse Trees

Anudhyan Boral, Sylvain Schmitz
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word according to a context-free grammar.  ...  We put forward the adequacy of propositional dynamic logic (PDL) on trees in these applications, and study as a sanity check the complexity of the corresponding model-checking problem: although complete  ...  Acknowledgments The authors thank the anonymous reviewers for their helpful comments; in particular for pointing out that the PDL tree formula in Example 5 could be expressed in XPath 1.0.  ... 
doi:10.1109/lics.2013.21 dblp:conf/lics/BoralS13 fatcat:orwfonyolbgmxkwoceoyldigra

Strong Completeness and Limited Canonicity for PDL

Gerard Renardel de Lavalette, Barteld Kooi, Rineke Verbrugge
2009 Journal of Logic, Language and Information  
Acknowledgment We thank Professor Goldblatt for pointing out these mistakes to us.  ...  In particular, Theorem 13.12 on first-order dynamic logic in Goldblatt (1987) straightforwardly leads to the Lindenbaum Lemma for PDL ω .  ...  For PDL ω , the property for programs and the formula property have to be proved via simultaneous induction.  ... 
doi:10.1007/s10849-009-9083-z fatcat:5foskcl44bfnnlxbziv7cduzo4

XPath with Conditional Axis Relations [chapter]

Maarten Marx
2004 Lecture Notes in Computer Science  
This paper is about the W3C standard node-addressing language for XML documents, called XPath. XPath is still under development.  ...  With it we can express paths specified by for instance "do a child step, while test is true at the resulting node".  ...  XCPath is expressively complete for first order properties on node labeled sibling ordered trees.  ... 
doi:10.1007/978-3-540-24741-8_28 fatcat:xdemxjaibfehdlga72ia6y66iu

Propositional Dynamic Logic for Higher-Order Functional Programs [chapter]

Yuki Satake, Hiroshi Unno
2018 Lecture Notes in Computer Science  
We present an extension of propositional dynamic logic called HOT-PDL for specifying temporal properties of higher-order functional programs.  ...  between call and return events, and the other for capturing higher-order control flow involving a function that is passed to or returned by a higher-order function.  ...  Acknowledgments We would like to thank anonymous referees for their useful comments. This work was supported by JSPS KAKENHI Grant Numbers 15H05706, 16H05856, 17H01720, and 17H01723.  ... 
doi:10.1007/978-3-319-96145-3_6 fatcat:j2i7ykn6jfdsrm6xyfuzslrvyq

Wreath Products of Forest Algebras, with Applications to Tree Logics

Mikolaj Bojanczyk, Howard Straubing, Igor Walukiewicz
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science  
These include the temporal logics CTL and EF, and first-order logic over the ancestor relation.  ...  We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics.  ...  See [3] for the definition. A. First-order logic for trees and forests Let A be a finite alphabet.  ... 
doi:10.1109/lics.2009.40 dblp:conf/lics/BojanczykSW09 fatcat:aeygynsizve4teegrpuuizpaoi

Infinite State Model-Checking of Propositional Dynamic Logics [chapter]

Stefan Göller, Markus Lohrey
2006 Lecture Notes in Computer Science  
Model-checking problems for propositional dynamic logic (PDL) and its extension PDL ∩ (which includes the intersection operator on programs) over various classes of infinite state systems (BPP, BPA, pushdown  ...  Precise upper and lower bounds are shown for the data/expression/combined complexity of these model-checking problems.  ...  We are confident that our upper bounds for PDL ∩ from Theorem 3 can be extended to this logic.  ... 
doi:10.1007/11874683_23 fatcat:6ntghigerfcr3bedtowmtc2bqi

Propositional Dynamic Logic with Recursive Programs [chapter]

Christof Löding, Olivier Serre
2006 Lecture Notes in Computer Science  
We show that the satisfiability problem for this extension remains decidable, generalising known decidability results for extensions of PDL by non-regular programs.  ...  We extend the propositional dynamic logic PDL of Fischer and Ladner with a restricted kind of recursive programs using the formalism of visibly pushdown automata (Alur, Madhusudan 2004).  ...  In order to capture more complex programs, several extensions of PDL have been considered.  ... 
doi:10.1007/11690634_20 fatcat:ocnydetcobdknjl3azko73i2ha

Propositional dynamic logic with recursive programs

Christof Löding, Carsten Lutz, Olivier Serre
2007 The Journal of Logic and Algebraic Programming  
Madhusudan, Visibly pushdown languages, in: We show that the satisfiability problem for this extension remains decidable, generalising known decidability results for extensions of PDL by non-regular programs  ...  In [11] it is shown that even adding only a single context-free program can lead to undecidability: the logic PDL + a # ba # is undecidable, where PDL + L stands for the extension of PDL, which allows  ...  Such paths may overlap and the tree automaton would have to keep track of which Vpas to simulate in order to check the diamond property for several nodes.  ... 
doi:10.1016/j.jlap.2006.11.003 fatcat:ytjzzbg27vadhkjuxulwbr6fsu

Propositional dynamic logic of looping and converse is elementarily decidable

Robert S. Streett
1982 Information and Control  
In order to establish this result, deterministic two-way automata on infinite trees are defined, and it is shown how they can be simulated by nondeterministic one-way automata.  ...  The satisfiability problem for propositional dynamic logic of looping and converse is then reduced to the emptiness problem for these two-way automata.  ...  Let F a be an automaton on infinite trees which, for every node x not labelled with Aa, runs the automaton Ea down every path from x in order to reject any tree containing a path from x which a repeatedly  ... 
doi:10.1016/s0019-9958(82)91258-x fatcat:sxeq4mxx4jchtdc4jmutwv5bzu

Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

Markus Latte
2011 Electronic Proceedings in Theoretical Computer Science  
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular.  ...  For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques.  ...  For PDL and PDL[REG] these tree-automata are finite-state [23] , for PDL [VPL] they are visibly pushdown tree-automata [14, 17] and for PDL [DCFL] and PDL[CFL] they are tree-automata with unbounded  ... 
doi:10.4204/eptcs.54.15 fatcat:wspdrut6zzb4thra4hfc2grf3u
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