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Use of OWL within the Gene Ontology [article]

Christopher J Mungall, Heiko Dietze, David Osumi-Sutherland
2014 bioRxiv   pre-print
Commonly conceived of as a simple terminology structured as a directed acyclic graph, the GO is actually well-axiomatized in OWL and is highly dependent on the OWL tool stack.  ...  The Gene Ontology (GO) is a ubiquitous tool in biological data analysis, and is one of the most well-known ontologies, in or outside the life sciences.  ...  a gene in one species based on the function of the equivalent gene in another species.  ... 
doi:10.1101/010090 fatcat:p52kbvqufzfpjnvecwoss4iygm

Modeling and Inferring on Role-Based Access Control Policies Using Data Dependencies [chapter]

Romuald Thion, Stéphane Coulondre
2006 Lecture Notes in Computer Science  
We focused on using Constrained Tuple-Generating Dependencies (CTGDs), a class of dependencies which includes traditional other ones.  ...  There is a serious need for administration tools allowing analysis and inference on access control policies.  ...  A promising opening to the use of CTGDs for access control modeling purpose are the results exposed in [18] . Their paper propose a new kind of dependencies subsumming CTGDs : Disjunctive-CTGDs.  ... 
doi:10.1007/11827405_89 fatcat:gzrtnjvlgvh5febdnsgvwqo2r4

Page 29 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
We give a new proof of the following result of Kreisel and Girard: Any function defined by a proof of Vx Sy Spec(x,y) is bounded by a function G,, of the hierarchy with a below the Bachmann-Howard ordinal  ...  These bounds de- pend only on the height of the deduction and on the number of inferences it contains.  ... 

Semantic management of middleware

Daniel Oberle
2004 Proceedings of the 1st international doctoral symposium on Middleware -  
The Ph.D. proposal addresses the complexity of building distributed applications and systems with Application Servers and Web Services middleware, respectively.  ...  The ontology captures properties of, relationships between and behaviors of the components and services that are required for management purposes.  ...  Also Mike Uschold from Boeing as well as the colleagues of the Won-derWeb projects for their fruitful hints.  ... 
doi:10.1145/1028480.1028484 dblp:conf/middleware/Oberle04 fatcat:4kku3lcqefav5e2f5dean5odue

Organizing Numerical Theories Using Axiomatic Type Classes

Lawrence C. Paulson
2004 Journal of automated reasoning  
Mathematical reasoning may involve several arithmetic types, including those of the natural, integer, rational, real and complex numbers. These types satisfy many of the same algebraic laws.  ...  Subtyping, where a type inherits properties from a supertype, can eliminate repetition only for a fixed type hierarchy set up in advance by implementors.  ...  Tobias Nipkow and Markus Wenzel equipped Isabelle with axiomatic type classes. The type classes for ordered rings and fields are based on earlier work by Gertrud Bauer and Wenzel.  ... 
doi:10.1007/s10817-004-3997-6 fatcat:muybtjzpmbburkh3l5w5hfrm4y

Shapiro Stewart. Second-order languages and mathematical practice. The journal of symbolic logic, vol. 50 (1985), pp. 714–742

Geoffrey Hellman
1989 Journal of Symbolic Logic (JSL)  
of relations on d and functions from d to d.  ...  Let L be a language. One purpose of the logic of L is to codify the correct inferences of L.  ... 
doi:10.2307/2275038 fatcat:fej2qgprz5aebeaamucxxbylwy

Page 1736 of Mathematical Reviews Vol. , Issue 80E [page]

1980 Mathematical Reviews  
Authors’ summary: “It is proved that even in the lowest class & of the Grzegorezyk hierarchy there exists a 3-ary function G such that any partial function f lies in the class =, of the arithmetic hierarchy  ...  Author’s summary: “We analyze the computational complexity of determining whether F is satisfiable when F is a formula of the classical predicate calculus (lacking identity and function symbols) which  ... 

Page 3545 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
We describe their axiomatic systems and algebraic varieties and show they can be suitably placed in a hierarchy of logics depending on their characteristic axioms.  ...  are constants c and d such that, for any function f from [A], the depth D(f) and complexity L(f) of f in the class of formulas over A are related by the relation D(f) < clog, L(f) + d.” 2004e:03050 03B52  ... 

The Complexity of Infinite Computations In Models of Set Theory

Olivier Finkel, Wolfgang Thomas
2009 Logical Methods in Computer Science  
second in one model of ZFC are \pi_2^0-sets, while in a different model of ZFC both are analytic but non Borel sets.  ...  We prove the following surprising result: there exist a 1-counter B\"uchi automaton and a 2-tape B\"uchi automaton such that the \omega-language of the first and the infinitary rational relation of the  ...  Acknowledgement I wish to thank the referees for their very useful comments on a preliminary version of this paper.  ... 
doi:10.2168/lmcs-5(4:4)2009 fatcat:p5b7skes2bd3nf7qvbnmiygusm

On the limit existence principles in elementary arithmetic and Σn0-consequences of theories

Lev D. Beklemishev, Albert Visser
2005 Annals of Pure and Applied Logic  
We also prove that the same principle, formulated as an inference rule, provides an axiomatization of the Σ 2 -consequences of IΣ 1 .  ...  This result, however, cannot be much improved: by adapting a theorem of D. Zambella and G. Mints we show that the logic of Π 1 -conservativity of primitive recursive arithmetic properly extends ILM.  ...  Joosten for useful comments and proof reading and G. Mints for a kind permission to include one of his results.  ... 
doi:10.1016/j.apal.2005.05.005 fatcat:gkxbfaxtircybhyh5p4n2hooku

From fuzzy logic to fuzzy mathematics: A methodological manifesto

Libor Běhounek, Petr Cintula
2006 Fuzzy sets and systems (Print)  
The paper states the problem of fragmentation of contemporary fuzzy mathematics and the need of a unified methodology and formalism.  ...  We formulate several guidelines based on Hájek's methodology in fuzzy logic, which enable us to follow closely the constructions and methods of classical mathematics recast in a fuzzy setting.  ...  Many of these axiomatics are in fact semi-classical, being founded upon the notions of truth degrees and membership functions, which are merely a classical rendering of fuzzy sets.  ... 
doi:10.1016/j.fss.2005.10.011 fatcat:4zezmbqspzdbzhjx5qrhbeea5a

A terminological simplification transformation for natural language question-answering systems

David G. Stallard
1986 Proceedings of the 24th annual meeting on Association for Computational Linguistics -  
This simplification method utilizes the encoded knowledge and the limited inference-making capability of a taxonomic knowledge representation system to reduce the constituent structure of logical expressions  ...  The specific application is to the problem of mapping expressions of the meaning representation language to a database language capable of retrieving actual responses.  ...  This paper has also benefited from the comments of Ralph Weischedel and Jos De Bruin. Beth Groundwater of SAIC was patient enough to use the software this work produced.  ... 
doi:10.3115/981131.981164 dblp:conf/acl/Stallard86 fatcat:rqf6g2gu35elfm3n5y57mbn3fi

Automating meta-theory creation and system extension [chapter]

David Basin, Fausto Giunchiglia, Paolo Traverso
1991 Lecture Notes in Computer Science  
The rst function lifts the actual inference rules to axioms that comprise a theory of GETFOL's inference capabilities.  ...  Within the GETFOL system we have built a pair of functions that operate between the system's implementation and a theory about this implementation.  ...  A more complex and interesting kind of optimization is possible based on transforming the proof-structure component of derived inference rules to a direct syntactic representation of the inference function  ... 
doi:10.1007/3-540-54712-6_217 fatcat:4glzci7ekzfsxoi56d5nrdwxcq

The Lean mathematical library [article]

The mathlib Community
2019 arXiv   pre-print
Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on classical mathematics, extensive hierarchy of structures, use of large- and small-scale automation, and  ...  This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant.  ...  Acknowledgments We thank Jasmin Blanchette, Assia Mahboubi, Josef Urban, and the anonymous referees for their helpful comments and suggestions.  ... 
arXiv:1910.09336v2 fatcat:h6jfjdrbknhaxl7w34ffymyjfe

On the complexity of inductive inference

Robert P. Daley, Carl H. Smith
1986 Information and Control  
An axiomatization of the notion of the complexity of inductive inference is developed and several results are presented which both resemble and contrast with results obtainable for the axiomatic computational  ...  complexity of recursive functions.  ...  ACKNOWLEDGMENTS We are grateful to the Departments of Computer Science at the Universities of Pittsburgh, Maryland and Purdue for providing computer time.  ... 
doi:10.1016/s0019-9958(86)80042-0 fatcat:uxbsl6rcvjbvhcqoyk3okduplq
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