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A Term Rewriting System for Kuratowski's Closure-Complement Problem

Osama Al-Hassani, Quratul-Ain Mahesar, Claudio Sacerdoti Coen, Volker Sorge, Marc Herbstritt
2012 International Conference on Rewriting Techniques and Applications  
We present a term rewriting system to solve a class of open problems that are generalisations of Kuratowski's closure-complement theorem.  ...  We model these axioms as rewrite rules and construct a rewriting system that allows us to close some so far open variants of Kuratowski's problem by analysing several million inference steps on a typical  ...  Sambin that stated the generalised Kuratowski's closure-complement problem studied in this paper and personally brought it to the attention of the third author.  ... 
doi:10.4230/lipics.rta.2012.38 dblp:conf/rta/Al-HassaniMCS12 fatcat:rhjegihn6vhajb7wx3sk3phare

Infinitary rewriting: meta-theory and convergence

Stefan Kahrs
2007 Acta Informatica  
The resulting meta-theory is studied, leading to a revised notion of infinitary rewrite system. For these systems a method is devised to prove their convergence.  ...  When infinitary rewriting was introduced by Kaplan et. al. [9] at the beginning of the 1990s, its term universe was explained as the metric completion of a metric on finite terms.  ...  The problem seems a technicality, caused by our condition (ii) for rewrite rules when the third rule of the system is considered. However, there is indeed a slight problem with this rule.  ... 
doi:10.1007/s00236-007-0043-2 fatcat:2zwphoocujgfjkciatsm2cmz7e

Reasoning about Iteration in Gödel's Class Theory [chapter]

Johan Gijsbertus Frederik Belinfante
2003 Lecture Notes in Computer Science  
The intent is to use this approach for automated reasoning about a variety of applications of iteration using Mc-Cune's automated reasoning program Otter.  ...  A computer implementation of Gödel's algorithm for class formation in Mathematica TM was used to formulate definitions and theorems about iteration in Gödel's class theory.  ...  f[g[x]] in terms of the reifications of g.For the constructor complement, for instance, the formula reify[x, complement[y]] = Id • complement[reify[x, y]] allows one to express the reification of complement  ... 
doi:10.1007/978-3-540-45085-6_18 fatcat:4qjtzv3wu5dm3akk2dgbzlarjq

Recognizable Sets of Graphs, Hypergraphs and Relational Structures: A Survey [chapter]

Bruno Courcelle
2004 Lecture Notes in Computer Science  
The general framework of this research which associates tightly algebraic notions (equational and recognizable sets) and Monadic Second-Order logic (for defining sets and transformations of graphs, hypergraphs  ...  for defining the edge-complement of a graph).  ...  Context-free sets of graphs can be defined as equational sets, i.e. as components of least solutions of systems of recursive set equations, in a much easier way than in terms of graph rewriting sequences  ... 
doi:10.1007/978-3-540-30550-7_1 fatcat:pkfifmamb5h5rj7u4vib2r7p7u

Vertex-minors, monadic second-order logic, and a conjecture by Seese

Bruno Courcelle, Sang-il Oum
2007 Journal of combinatorial theory. Series B (Print)  
We also obtain a polynomial-time algorithm to check that the rank-width of a graph is at most k for any fixed k. The proofs use isotropic systems.  ...  We obtain a slight weakening of a conjecture by Seese stating that sets of graphs having a decidable satisfiability problem for monadic second-order logic have bounded clique-width.  ...  We thank the organizers, A. Brandstädt, D. Corneil, K. Jansen, and J. Spinrad for inviting us.  ... 
doi:10.1016/j.jctb.2006.04.003 fatcat:3dfb5tqexndablnknwykkbcdlu

Oriented components and their separations

Baerbel M R Stadler, Peter F. Stadler
2017 Applied General Topology  
Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches.  ...  The main result is a characterization of generalized reaches in terms of equivalent separation spaces.<br /><br /></p>  ...  The Wallace closure can be viewed as a generalization of Kuratowski's closure function for topologies. We will explore this connection to generalized topologies in forthcoming work.  ... 
doi:10.4995/agt.2017.5868 fatcat:3asfin2ravcsxpanbnuqwnec4u

Two theses of knowledge representation: Language restrictions, taxonomic classification, and the utility of representation services

Jon Doyle, Ramesh S. Patil
1991 Artificial Intelligence  
omitting constructs which require non-polynomial worst-case response times for sound and complete classification.  ...  Levesque and Brachman argue that in order to provide timely and correct responses in the most critical applications, general purpose knowledge representation systems should restrict their languages by  ...  We are specially indebted to Randall Davis and Peter Patel-Schneider for extensive, helpful comments on earlier drafts.  ... 
doi:10.1016/0004-3702(91)90029-j fatcat:zxvnt4bmj5gyxlmvxvd7hrtiea

A Markov process for an infinite interacting particle system in the continuum [article]

Yuri Kozitsky, Michael Röckner
2021 arXiv   pre-print
in Γ that solves a restricted initial-value martingale problem for the mentioned system.  ...  For a special class 𝒫_ exp of (sub-Poissonian) probability measures on Γ, we prove the existence of a unique family {P_t,μ: t≥ 0, μ∈𝒫_ exp} of probability measures on the space of cadlag paths with values  ...  He thanks also Lucian Beznea and BIT DEFENDER for warm hospitality and financial support during his stay in Bucharest in April 2019, where a part of this work was done.  ... 
arXiv:1912.00964v2 fatcat:qdftcsfbijbjrhoqoxvj4lnanq

A Markov process for an infinite interacting particle system in the continuum

Yuri Kozitsky, Michael Röckner
2021 Electronic Journal of Probability  
in Γ that solves a restricted initial-value martingale problem for the mentioned system.  ...  E l e c t r o n i c J o u r n a l o f P r o b a b i l i t y Electron. Abstract An infinite system of point particles placed in R d is studied.  ...  He thanks also Lucian Beznea and BIT DEFENDER for warm hospitality and financial support during his stay in Bucharest in April 2019, where a part of this work was done.  ... 
doi:10.1214/21-ejp631 fatcat:cy2f6yjyujevxdkxv4nmbtpvgi

Guaranteed estimates for the length of branches of periodic orbits for equivariant Hopf bifurcation [article]

E. Hooton, Z. Balanov, D. Rachinskii
2020 arXiv   pre-print
A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the assumption that the nonlinear terms satisfy a linear estimate in a ball.  ...  Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered.  ...  Acknowledgments This work has been done as a part of the Prospective Human Resources Support Program of the Czech Academy of Sciences; EH acknowledges the support by this program.  ... 
arXiv:2002.03457v1 fatcat:3hr2dp4w5nhltmedxbxxlskroe

E-values: Calibration, combination, and applications [article]

Vladimir Vovk, Ruodu Wang
2020 arXiv   pre-print
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values.  ...  This allows us to develop efficient procedures using e-values for testing multiple hypotheses.  ...  Acknowledgments The authors thank Aaditya Ramdas, Alexander Schied, and Glenn Shafer for helpful suggestions.  ... 
arXiv:1912.06116v4 fatcat:6qexl46x2rekpn5q4wnn6anm5u

Complete Additivity and Modal Incompleteness [article]

Wesley H. Holliday, Tadeusz Litak
2018 arXiv   pre-print
In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to V-BAOs, namely the provability logic GLB.  ...  The story weaves together a paper of van Benthem, 'Syntactic aspects of modal incompleteness theorems,' and a longstanding open question: whether every normal modal logic can be characterized by a class  ...  32 We thank Mamuka Jibladze for the first problem and Sam van Gool for the second. In the latter case, we also appreciate email discussions with Mai Gehrke and Marcel Erné.  ... 
arXiv:1809.07542v1 fatcat:priuo4blnjhozdoajxxfyy6f6y

A logician's view of graph polynomials [article]

J.A. Makowsky and E.V. Ravve and T. Kotek
2018 arXiv   pre-print
Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates.  ...  The paper emphasizes a model theoretic view and gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the  ...  Acknowledgment The authors would like to thank Petter Brändén for guiding us to the literature of stable polynomials, and Jason Brown and four anonymous readers of an earlier version of this paper for  ... 
arXiv:1703.02297v2 fatcat:4e3eyz4rh5fzjbjqjbmnjpqy5e

Algorithmic Meta-Theorems [article]

Stephan Kreutzer
2009 arXiv   pre-print
Algorithmic meta-theorems are general algorithmic results applying to a whole range of problems, rather than just to a single problem alone.  ...  They often have a "logical" and a "structural" component, that is they are results of the form: every computational problem that can be formalised in a given logic L can be solved efficiently on every  ...  Many thanks to Javier Esparza for proofreading this manuscript and for his patience as an editor.  ... 
arXiv:0902.3616v1 fatcat:wsuguljgrvfndhxlsps2ibes2i

Map Genus, Forbidden Maps, and Monadic Second-Order Logic

B. Courcelle, V. Dussaux
2002 Electronic Journal of Combinatorics  
A map is a graph equipped with a circular order of edges around each vertex. These circular orders represent local planar embeddings.  ...  The genus of a map is the minimal genus of an orientable surface in which it can be embedded.  ...  Schaeffer for helpful remarks.  ... 
doi:10.37236/1656 fatcat:oig6oqavprac3pkwafadhpl5iu
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