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The succinctness of first-order logic on linear orders

Martin Grohe, Nicole Schweikardt, Andrei Voronkov
2005 Logical Methods in Computer Science  
We study the succinctness of logics on linear orders. Our first theorem is concerned with the finite variable fragments of first-order logic.  ...  Our second main result compares the succinctness of first-order logic on linear orders with that of monadic second-order logic.  ...  The fragment of monadic second-order logic that has the same expressiveness as first-order logic on linear orders is non-elementarily more succinct than first-order logic.  ... 
doi:10.2168/lmcs-1(1:6)2005 fatcat:bxwtbrbvsjbwjlctipgcicxx2m

The succinctness of first-order logic on linear orders

M. Grohe, N. Schweikardt
2004 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.  
Our second main result compares the succinctness of first-order logic on linear orders with that of monadic second-order logic.  ...  We study the succinctness of logics on linear orders that have the same expressive power as first-order logic. Our first theorem is concerned with the finite variable fragments of first-order logic.  ...  The fragment of monadic second-order logic that has the same expressiveness as first-order logic on linear orders is non-elementarily more succinct than firstorder logic.  ... 
doi:10.1109/lics.2004.1319638 dblp:conf/lics/GroheS04 fatcat:hxb2elrinzhcdn4d7f4evapsn4

Comparing the succinctness of monadic query languages over finite trees

Martin Grohe, Nicole Schweikardt
2004 RAIRO - Theoretical Informatics and Applications  
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees.  ...  Succinctness of the languages is closely related to the combined and parameterized complexity of query evaluation for these languages.  ...  For example, Kamp's well know theorem states that first-order logic and linear time temporal logic have the same expressive power on strings [Kam68] , but there is no elementary translation from first-order  ... 
doi:10.1051/ita:2004017 fatcat:s4nxmdzsorbfxoy5w4o657oqxi

Comparing the Succinctness of Monadic Query Languages over Finite Trees [chapter]

Martin Grohe, Nicole Schweikardt
2003 Lecture Notes in Computer Science  
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees.  ...  Succinctness of the languages is closely related to the combined and parameterized complexity of query evaluation for these languages.  ...  For example, Kamp's well know theorem states that first-order logic and linear time temporal logic have the same expressive power on strings [Kam68] , but there is no elementary translation from first-order  ... 
doi:10.1007/978-3-540-45220-1_20 fatcat:psdjunqwiffs7j4u7jjhuvkdcq

Expressivity and Succinctness of Order-Invariant Logics on Depth-Bounded Structures [chapter]

Kord Eickmeyer, Michael Elberfeld, Frederik Harwath
2014 Lecture Notes in Computer Science  
We study the expressive power and succinctness of orderinvariant sentences of first-order (FO) and monadic second-order (MSO) logic on graphs of bounded tree-depth.  ...  We show that for every order-invariant FO sentence there exists an FO sentence whose size is elementary in the size of the original sentence, and whose number of quantifier alternations is linear in the  ...  We want to thank Isolde Adler for bringing the first two authors together with the third author, and Nicole Schweikardt for her helpful suggestions.  ... 
doi:10.1007/978-3-662-44522-8_22 fatcat:iiqimt7otjfg3eh5xxqol62xum

Navigational XPath

Balder ten Cate, Maarten Marx
2007 SIGMOD record  
We survey expressivity results for navigational fragments of XPath 1.0 and 2.0, as well as Regular XPath ≈ . We also investigate algebras for these fragments.  ...  In [26] , an axiomatization of first-order logic on XMLtrees is given, from which an axiomatization for TRA on XML-trees is derived.  ...  We will answer this question by mapping each XPath dialect to an equally expressive variant of first-order logic.  ... 
doi:10.1145/1328854.1328858 fatcat:kjouhgo2pnhftj26aj5vzovxhe

Expressiveness of Hybrid Temporal Logic on Data Words

Ahmet Kara, Thomas Schwentick
2011 Electronical Notes in Theoretical Computer Science  
Hybrid temporal logic (HTL) on data words can be considered as an extension of the logic LTL ↓ introduced by Demri and Lazic [3] .  ...  The paper further studies the succinctness of HTL in comparison with LTL ↓ and shows that the number-of-variables hierarchy of HTL is infinite.  ...  Expressiveness The expressive power of HTL on data words coincides with the expressive power of first-order logic (FO).  ... 
doi:10.1016/j.entcs.2011.10.010 fatcat:64bs54hzsjgzjm3aqvlhhs72qm

BTL2 and the expressive power of ECTL+

Alexander Rabinovich, Philippe Schnoebelen
2006 Information and Computation  
BTL 2 is the branching-time logic with arbitrary quantification over paths, and where path formulae are restricted to quantifier depth 2 first-order formulae in the monadic logic of order.  ...  We show that ECTL + , the classical extension of CTL with fairness properties, is expressively equivalent to BTL 2 , a natural fragment of the monadic logic of order.  ...  Second-order monadic logic of order The syntax of MLO , the second-order monadic logic of order, has in its vocabulary individual first-order variables x 0 , x 1 , x 2 , . . .  ... 
doi:10.1016/j.ic.2005.07.006 fatcat:zod5kml4vzgubjlobu7gbsvtq4

On Expressive Completeness of Duration and Mean Value Calculi (Extended Abstract)

Alexander Rabinovich
1997 Electronical Notes in Theoretical Computer Science  
Finally, we show that there exists at least an exponential gap between the succinctness of the propositional duration (mean value) calculus and that of monadic rst-order logic of order.  ...  This paper compares the expressive power of rst-order monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of two formalisms for the speci cation  ...  Acknowledgement I w ould like to thank the anonymous referees for their helpful suggestions.  ... 
doi:10.1016/s1571-0661(05)80476-1 fatcat:imuhell3zjatbjiuj5yfh5qmje

Probabilistic verification and approximation

Richard Lassaigne, Sylvain Peyronnet
2008 Annals of Pure and Applied Logic  
Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas.  ...  We study the existence of efficient approximation methods to verify quantitative specifications of probabilistic systems.  ...  Acknowledgements We would like to thank Thomas Hérault for his important participation to the development of APMC, and an anonymous referee for his pertinent remarks and suggestions.  ... 
doi:10.1016/j.apal.2007.11.006 fatcat:kjhhgvh6prglxehlpepy42afju

A Framework for Reasoning about Dynamic Axioms in Description Logics

Bartosz Bednarczyk, Stephane Demri, Alessio Mansutti
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
In the paper, we focus on ALC and EL augmented with dynamic axioms, or to their subclass of positive dynamic axioms.  ...  means to predict the evolution of interpretations.  ...  Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2020/229 dblp:conf/ijcai/CepekC20 fatcat:yyqxfkdhubfodizp54uqci4tee

Probabilistic Verification and Approximation

Richard Lassaigne, Sylvain Peyronnet
2006 Electronical Notes in Theoretical Computer Science  
Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas.  ...  We study the existence of efficient approximation methods to verify quantitative specifications of probabilistic systems.  ...  Acknowledgements We would like to thank Thomas Hérault for his important participation to the development of APMC, and an anonymous referee for his pertinent remarks and suggestions.  ... 
doi:10.1016/j.entcs.2005.05.031 fatcat:usjmmp4kjzdrnoztoxpskrguka

On the Compilation of Stratified Belief Bases under Linear and Possibilistic Logic Policies

Salem Benferhat, Safa Yahi, Habiba Drias
2007 International Joint Conference on Artificial Intelligence  
This paper focuses on the well-known linear order and possibilistic logic strategies.  ...  In particular, the number of additional variables, that are added to original stratified bases, corresponds exactly to the number of priority levels existing in the base.  ...  Acknowledgments: This work is supported by the national project ANR Blanc MICRAC (Modèles informatiques et cognitifs du raisonnement causal).  ... 
dblp:conf/ijcai/BenferhatYD07 fatcat:ij3ap5gdvjemtfkg33534pie6u

Marrying words and trees

Rajeev Alur
2007 Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '07  
In particular, we show that finite-state nested word automata can be exponentially more succinct than tree automata, and pushdown nested word automata include the two incomparable classes of contextfree  ...  In particular, we show that finite-state nested word automata can be exponentially more succinct than tree automata, and pushdown nested word automata include the two incomparable classes of context-free  ...  asked questions regarding the relationship between ordered trees and nested words.  ... 
doi:10.1145/1265530.1265564 dblp:conf/pods/Alur07 fatcat:b7vngz22jjfphl34futklrdoei

Page 2668 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
Summary: “We introduce a new class OrtSP of first-order sequen- tial programs.  ...  The method was explicitly stated as a first-order consistency proof in the case of pure equational, constructor-based specifications.  ... 
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