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Arity hierarchy for temporal logics

Alexander Rabinovich
2008 Theoretical Computer Science  
which uses modalities of arity less than n.  ...  The main result states that in contrast to Kamp's Theorem, for every n there is a modality of arity n definable by a monadic logic formula, which is not equivalent over trees to any temporal logic formula  ...  Arity Hierarchy over ω: Is TLAR r less expressive than TLAR r+1 over the class of ω-chains?  ... 
doi:10.1016/j.tcs.2008.06.006 fatcat:4qy6yzt6orb3tbamywitzlian4

The Arity Hierarchy in the Polyadic μ-Calculus

Martin Lange
2015 Electronic Proceedings in Theoretical Computer Science  
In this paper we show a hierarchy result with respect to expressive power inside the polyadic mu-calculus: for every level of fixpoint alternation, greater arity of relations gives rise to higher expressive  ...  Consequently, we obtain an arity hierarchy relative to the alternation hierarchy.  ...  The Arity Hierarchy The Principle Construction The aim of this section is to show that L 1 µ , L 2 µ , . . . forms a strict hierarchy with respect to expressive power.  ... 
doi:10.4204/eptcs.191.10 fatcat:oi5irp6ef5fd3getjjvgiiit2m

A double arity hierarchy theorem for transitive closure logic

Martin Grohe, Lauri Hella
1996 Archive for Mathematical Logic  
As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers  ...  The arity hierarchies of the corresponding quantifiers are strict by our theorem. • The arity hierarchy of the Hamiltonian path quantifier Q HP is strict.  ...  Consequently, in this case we say that the arity hierarchy of Q C is strong. Note that we actually proved that the arity hierarchies of Q T C and Q DT C * are strong.  ... 
doi:10.1007/bf01268616 fatcat:jzilabwfofcytdi33oab7uvm5i


Guozhu Dong, Louxin Zhang
2000 International Journal of Foundations of Computer Science  
In fact, there is a query, over input relations of arity 3k + 1, in FOIES k ? FOIES k?1 .  ...  However, that separation was achieved using queries having input relations of arity at least 6k.  ... 
doi:10.1142/s0129054100000302 fatcat:oruvnxpdmnawvhbxdcdeyypqlq

Page 8497 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
We show that the arity hierarchy in this case is also strict.  ...  The positions of queries in the two arity-based hierarchies can differ; we give the positions in this hierarchy of the queries considered for the other arity hierarchy.” © 1998 Academic Press {For the  ... 

Arity and alternation in second-order logic

J.A. Makowsky, Y.B. Pnueli
1996 Annals of Pure and Applied Logic  
We show that this imposes a proper hierarchy on second-order logic, i.e. for every k, n there are problems not definable in AA(k, n) but definable in AA(k + cl, n + d,) for some cl, d,.  ...  Let SAA@, n)(AA(k, n)) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of (both first-order and) second-order quantification  ...  We define now hierarchies AAZ(k, n) , AAII(k, n) , AA(k, n) , the strict AA-Hierarchy (alternation-arity hierarchy) and SAAC(k, n) , SAAII(k, n) , SAA(k, n) , the second-order AA-Hierarchy (alternation-urity  ... 
doi:10.1016/0168-0072(95)00013-5 fatcat:b3iwj3l4sze6plwzp7jw2nmvsu

Incremental recomputation of recursive queries with nested sets and aggregate functions [chapter]

Leonid Libkin, Limsoon Wong
1998 Lecture Notes in Computer Science  
This is again in sharp contrast to maintenance in relational calculus, which admits a strict arity-based hierarchy.  ...  We also show that one does not need auxiliary relations of arity more than 2.  ...  Since the arity hierarchy collapses in the presence of simple extensions such as aggregate functions as in IES(SQL) k , we feel that a hierarchy based on arities is not robust and not natural for incremental  ... 
doi:10.1007/3-540-64823-2_13 fatcat:h55jvl63t5c5xftwxdxcscckae

About the relation between spatial subdivisions and object hierarchies used in ray tracing

Vlastimil Havran
2007 Proceedings of the 23rd Spring Conference on Computer Graphics - SCCG '07  
In this paper we study the relation between object hierarchies (such as bounding volume hierarchies) and spatial subdivisions (such as kd-trees and octrees) in the context of ray tracing for static scenes  ...  Second, we show how kd-trees can be emulated via bounding volume hierarchies. More importantly we show how bounding volume hierarchies can be emulated via kd-trees in six-dimensional space.  ...  Relation between Object Hierarchies and Spatial Subdivisions In Section 3 we have discussed the properties of spatial subdivisions in dependence on their arity.  ... 
doi:10.1145/2614348.2614355 dblp:conf/sccg/Havran07 fatcat:msqa5an4zbg23owsc56z6p3kku

Towards Design Formalization to Support Reuse in ECAD Frameworks [chapter]

Joachim Altmeyer, Bernd Schuermann, Martin Schuetze
1995 Electronic Design Automation Frameworks  
For instance, a feature 'Arity is 4' is a specialization of a feature 'Arity is Even', i.e. 'Arity is 4' < 'Arity is Even'.  ...  Example 1 (design hierarchy) In figure 4 , the design hierarchy is illustrated by an example using the PLAYOUT design system [Zim89] .  ... 
doi:10.1007/978-0-387-34880-3_23 fatcat:5r6aubgapbgkzdlzlnk6ruitsa

Horn tables-an efficient tool for handling incomplete information in databases

G. Grahne
1989 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '89  
The representation hierarchy. THE COMPLEXITY OF QUERY EVALUATION A query q of arity (ai, . . . . a,,) + (bt, . . . . b,,,) is a mapping from instances to instances of the appropriate arities.  ...  An instance I of arity (n) satisjies a dependency c of arity (n) if I is a model (in the sence of mathematical logic) of the sentence.  ... 
doi:10.1145/73721.73728 dblp:conf/pods/Grahne89 fatcat:l4xv6tkynbgg3mnzvuldyffrji

Multi-Method Dispatch Using Multiple Row Displacement [chapter]

Candy Pang, Wade Holst, Yuri Leontiev, Duane Szafron
1999 Lecture Notes in Computer Science  
The first example uses the type hierarchy and 2-arity method definitions from Figure 5 (a).  ...  Figure 2 presents a sample inheritance hierarchy H and its induced 2-arity product-type graph, H 2 .  ... 
doi:10.1007/3-540-48743-3_14 fatcat:iqfkazfo45embkvdlknthhtrhe

Modeling hierarchy using symbolic regression

Ilknur Icke, Joshua C. Bongard
2013 2013 IEEE Congress on Evolutionary Computation  
Here we present a symbolic regression method that detects and captures hidden hierarchy in a given system.  ...  Accordingly, the h1 and h2 algorithms start to lose their advantage in faithfully modeling the hierarchy as the arity increases.  ...  5000 randomly generated stimuli creating a 5000x((arity layers − 1)/(arity − 1)) dataset.  ... 
doi:10.1109/cec.2013.6557932 dblp:conf/cec/IckeB13a fatcat:qk5l3ka4mndxddjeyowhbt5kju

Arity Bounds in First-Order Incremental Evaluation and Definition of Polynomial Time Database Queries

Guozhu Dong, Jianwen Su
1998 Journal of computer and system sciences (Print)  
The positions of queries in the two arity-based hierarchies can differ; we give the positions in this hierarchy of the queries considered for the other arity hierarchy. ]  ...  We show that the arity hierarchy in this case is also strict.  ...  It should be pointed out that for the small arities the hierarchies are separated using graph queries, whereas for large arities the hierarchies are separated using queries over relations with large arities  ... 
doi:10.1006/jcss.1998.1565 fatcat:52nhopb6wfajnhtcl4zcfws6ci

Hierarchies in inclusion logic with lax semantics [article]

Miika Hannula
2014 arXiv   pre-print
Arity hierarchy is shown to be strict by relating the question to the study of arity hierarchies in fixed point logics.  ...  In case of universal quantifiers, the corresponding hierarchy collapses at the first level.  ...  ⊓ ⊔ Strictness of the Arity Hierarchy In this section we will show that the following strict arity hierarchy holds (already in finite models). Theorem 6.  ... 
arXiv:1401.3235v1 fatcat:tkxqiebtnbfnbhzd7ur25inw2e

Polish Notation

Taneli Huuskonen
2015 Formalized Mathematics  
We present some mathematical folklore about representing formulas in "Polish notation", that is, with operators of fixed arity prepended to their arguments.  ...  The Polish arity from list B yielding a Polish arity-function of T is defined by the term (Def. 30) the arity from list B.  ...  The Polish arity ϕ yielding a natural number is defined by the term (Def. 35) α(Polish-WFF-head ϕ). Let us consider n. Let ϕ be an element of the Polish-expression hierarchy(T , α, n).  ... 
doi:10.1515/forma-2015-0014 fatcat:m25fzpr3mjcshd4o7tnm56jiqy
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