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Constructing Order Type Graphs using an Axiomatic Approach [article]

Sergey Bereg, Mohammadreza Haghpanah
2020 arXiv   pre-print
We present a new class of geometric graphs, called OT-graphs, using abstract order types and their axioms described in the well-known book by Knuth . Each OT-graph corresponds to a unique order type.  ...  Recently, Aichholzer introduced exit graphs for visualizing order types in the plane.  ...  In many cases there are different OT-graphs of minimum size for the same order type. One can use other criteria to optimize OT-graphs, for example, crossings.  ... 
arXiv:2011.14282v1 fatcat:r4owo5toijegvadefj7euk3oxi

The Information Flow Framework: A Descriptive Category Metatheory [article]

Robert E. Kent
2011 arXiv   pre-print
Each metalevel services the levels below by providing a metalanguage used to declare and axiomatize those levels.  ...  It is an experiment in foundations, which follows a bottom-up approach to logical description. The IFF forms the structural aspect of the IEEE P1600.1 Standard Upper Ontology (SUO) project.  ...  The important submodules in the FOL axiomatization are the following: a term/tuple fixpoint axiomatization, an expression/arity fixpoint axiomatization, the Lawvere construction axiomatization, an axiomatization  ... 
arXiv:1108.4133v1 fatcat:fokkbpvyyrhbhhrf6ixzsac7lm

Page 2180 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
In part III the authors continue to construct a nonlocal quantum field theory in the strong language of functional analysis using the modified Bogolyubov axiomatic approach.  ...  Such an axiomatization is used in the correct formulation of the axiom of complexly broken microcausality in the nonlocal quantum theory.  ... 

Axiomatic Criteria for Quotients and Subobjects for Higher-Order Data Types [chapter]

Jo Hannay
2003 Lecture Notes in Computer Science  
This generalises the method to handle data types with higher-order operations, using standard simulation relations. We also give a direct setoid-based model satisfying the criteria.  ...  Axiomatic criteria are given for the existence of higher-order maps over subobjects and quotients.  ...  We have devised and validated a method in logic for proving specification refinement for data types with higher-order operations.  ... 
doi:10.1007/3-540-45061-0_70 fatcat:yaulrbahwbbebmqq4ilkagsi2a

Metaphors of Order and Disorder: From the Tree to the Labyrinth and Beyond

Gian Carlo Fedeli
2013 Knowledge organization  
, I will try to identify common themes and differences in the transition from a semantic domain expression of confusion or uncertainty (labyrinth, map) to a semantic domain in which metaphors express ordering  ...  , and which were initially adopted, especially during the early modern period, to highlight the impossibility of building a reference system capable of guiding a user through the complex encyclopedic order  ...  using graph theory, are capable of representing their own spatial order.  ... 
doi:10.5771/0943-7444-2013-6-375 fatcat:delv6ec45jdljhkelplepiabe4

Implementing hash-consed structures in Coq [article]

Thomas Braibant, Jacques-Henri Jourdan (INRIA Rocquencourt), David Monniaux
2013 arXiv   pre-print
We report on three different approaches to use hash-consing in programs certified with the Coq system, using binary decision diagrams (BDD) as running example.  ...  There are different trade-offs between faithful use of pristine extracted code, and code that is fine-tuned to make use of OCaml programming constructs not available in Coq.  ...  Yet, one could also expose unique identifiers in the "smart constructor" approach by stating as axioms that there exists an injection from the BDD nodes to a totally ordered type of unique identifiers.  ... 
arXiv:1304.6038v1 fatcat:wxvcwzn33vd4dbbvhfiexmjhme

Semantic Integration in the IFF [article]

Robert E. Kent
2011 arXiv   pre-print
The IFF maintains ontologies using powerful composition primitives, which includes the fusion construction.  ...  The IEEE P1600.1 Standard Upper Ontology (SUO) project aims to specify an upper ontology that will provide a structure and a set of general concepts upon which domain ontologies could be constructed.  ...  Hence, this approach to alignment uses logics, not just theories. types as a single type in a mediating or reference theory, with two mappings from this new type back to the participant theory types.  ... 
arXiv:1109.0032v1 fatcat:nriez7m6ejelncwlfg5tkplwhm

Realms: A Structure for Consolidating Knowledge about Mathematical Theories [article]

Jacques Carette, William M. Farmer, Michael Kohlhase
2014 arXiv   pre-print
We also give an outline of the mechanisms that are needed to create and maintain realms.  ...  A realm contains several axiomatizations of a theory that are separately developed.  ...  The first kind are axiomatizations of a complete ordered field -all complete ordered fields are isomorphic. The second kind are constructions of the real numbers, of which there are many.  ... 
arXiv:1405.5956v1 fatcat:wl7jhafgcfelziasv6bmunzynq

Implementing Hash-Consed Structures in Coq [chapter]

Thomas Braibant, Jacques-Henri Jourdan, David Monniaux
2013 Lecture Notes in Computer Science  
We report on three different approaches to use hash-consing in programs certified with the Coq system, using binary decision diagrams (BDD) as running example.  ...  There are different trade-offs between faithful use of pristine extracted code, and code that is fine-tuned to make use of OCaml programming constructs not available in Coq.  ...  Yet, one could also expose unique identifiers in the "smart constructor" approach by stating as axioms that there exists an injection from the BDD nodes to a totally ordered type of unique identifiers.  ... 
doi:10.1007/978-3-642-39634-2_36 fatcat:gljdvzgtu5ahtd2rsjg67smhjy

Attack Trees with Sequential Conjunction [chapter]

Ravi Jhawar, Barbara Kordy, Sjouke Mauw, Saša Radomirović, Rolando Trujillo-Rasua
2015 IFIP Advances in Information and Communication Technology  
We give a semantics to SAND attack trees by interpreting them as sets of series-parallel graphs and propose a complete axiomatization of this semantics.  ...  This operator enables the modeling of ordered events.  ...  The second approach is to introduce a mechanism for ordering events in an attack tree, for instance by adding a new type of edge to express causality or conditionality.  ... 
doi:10.1007/978-3-319-18467-8_23 fatcat:nydlgfds2fhn7faykeoun3joyu

IMPS: An updated system description [chapter]

William M. Farmer, Joshua D. Guttman, F. Javier Thayer Fábrega
1996 Lecture Notes in Computer Science  
The system consists of a library of axiomatic theories and a collection of tools for exploring and extending the mathematics embodied in the theory library.  ...  Reference [10] presents an overview of the system. The imps system has changed little since Version 1.2 was released in July 1994.  ...  It axiomatizes the reals as a complete ordered field, using a second-order axiom to express completeness.  ... 
doi:10.1007/3-540-61511-3_94 fatcat:r4eliqpm5vcmppts65uzolngpa

An Ontology for Formal Models of Kinship [chapter]

Carmen Chui, Michael Grüninger, Janette Wong
2020 Frontiers in Artificial Intelligence and Applications  
Based on these algebraic models, we provide an ontology for kinship written in first-order logic and demonstrate how the ontology can be used to validate definitions found in Canadian legal laws and data  ...  The approach we have taken to axiomatize T kinship is independent of gender.  ...  the Hasse graph of the lattice-free partial ordering G.  ... 
doi:10.3233/faia200663 fatcat:bfc4e6ucuzbejdjxvk3rhcvvim

Theorem Reuse by Proof Term Transformation [chapter]

Einar Broch Johnsen, Christoph Lüth
2004 Lecture Notes in Computer Science  
The paper also considers how to reapply such abstracted theorems, and suggests an approach based on mappings between operations and types, and on systematically exploiting the dependencies between theorems  ...  This paper proposes an approach where theorems are generalised by abstracting their proofs from the original setting.  ...  Catesbeiana for pointing out potential pitfalls, and to Stefan Berghofer for explaining some technicalities of Isabelle's proof terms to us.  ... 
doi:10.1007/978-3-540-30142-4_12 fatcat:zxrdadywandvliggfkfdhzwrsy

Realms: A Structure for Consolidating Knowledge about Mathematical Theories [chapter]

Jacques Carette, William M. Farmer, Michael Kohlhase
2014 Lecture Notes in Computer Science  
We also give an outline of the mechanisms that are needed to create and maintain realms.  ...  A realm contains several axiomatizations of a theory that are separately developed.  ...  The first kind are axiomatizations of a complete ordered field. (All complete ordered fields are isomorphic.) The second kind are constructions of the real numbers, of which there are many.  ... 
doi:10.1007/978-3-319-08434-3_19 fatcat:vbuytxhm7ja6farniiuitmmpoa

IMPS: System description [chapter]

William M. Farmer, Joshua D. Guttman, F. Javier Thayer
1992 Lecture Notes in Computer Science  
Support for the Axiomatic Method. imps supports the "little theories" version of the axiomatic method, as opposed to the "big theory" version.  ...  In the little theories approach, reasoning is distributed over a network of theories.  ...  The little theories style of the axiomatic method is employed extensively in mathematical practice; in [4] , we discuss its benefits for mechanical theorem provers, and how the approach is used in imps  ... 
doi:10.1007/3-540-55602-8_207 fatcat:2o7adqrx6naufmeplnpk5jx43i
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