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Fragments of Spider Diagrams of Order and Their Relative Expressiveness [chapter]

Aidan Delaney, Gem Stapleton, John Taylor, Simon Thompson
2010 Lecture Notes in Computer Science  
We consider the expressiveness of spider diagrams of order (SDoO), which extend spider diagrams by including syntax that provides ordering information between elements.  ...  Fragments of SDoO are created by systematically removing each aspect of the syntax. We establish the relative expressiveness of the various fragments.  ...  Acknowledgements This research forms part of the the Defining Regular Languages with Diagrams (EPSRC grant EP/H012311/1) and Sketching Euler Diagrams (EPSRC grant EP/H048480/1) projects.  ... 
doi:10.1007/978-3-642-14600-8_10 fatcat:6h3jelafjncvbcrftt3e44xgc4

The Semiotics of Spider Diagrams

Jim Burton, John Howse
2017 Logica Universalis  
Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first order logic with equality.  ...  We examine the original goals of the designers, the ways in which the notation has evolved and its connection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce on which spider  ...  Thus, spider diagrams were first produced by removing syntax from constraint diagrams in order to define a decidable fragment which would make the task of formalising the more expressive notation tractable  ... 
doi:10.1007/s11787-017-0167-2 fatcat:j4ywlgct5bctllkv6hxcs7pjqy

Mixing Visual and Textual Constraint Languages [chapter]

Stuart Kent, John Howse
1999 Lecture Notes in Computer Science  
The goal of this work is to provide more intuitive and expressive languages to support the construction and presentation of rich and precise models.  ...  Constraint diagrams have been proposed as a means of notating similar constraints, but in a visual form.  ...  Thanks are also due to Steve Gaito and Niall Ross of Nortel Networks UK, and Yossi Gil of the Technion, Israel, for many valued discussions and feedback.  ... 
doi:10.1007/3-540-46852-8_28 fatcat:p3xcrnf22nbdtejve6s37imy3e

Deriving sound inference rules for concept diagrams

P. Chapman, G. Stapleton, J. Howse, I. Oliver
2011 2011 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)  
The process of designing and modelling an ontology can be difficult, especially if the user finds the syntax to be relatively inaccessible.  ...  We present a case study comprising: (a) a set of axioms for an ontology, and (b) a set of theorems that follow from the axioms, together with their proofs.  ...  ACKNOWLEDGEMENT: This research is supported by EP-SRC grants Defining Regular Languages with Diagrams EP/H012311 and Sketching Euler Diagrams EP/H048480.  ... 
doi:10.1109/vlhcc.2011.6070384 dblp:conf/vl/ChapmanSHO11 fatcat:ge2n67rlurcrlkacyx44hit4hq

On the Completeness of Spider Diagrams Augmented with Constants [chapter]

Gem Stapleton, John Howse, Simon Thompson, John Taylor, Peter Chapman
2013 Visual Reasoning with Diagrams  
We prove that this extended system is equivalent in expressive power to the language of spider diagrams without constants and, hence, equivalent to monadic first order logic with equality. r  ...  Several sound and complete spider diagram systems have been developed and it has been shown that they are equivalent in expressive power to monadic first order logic with equality.  ...  A formalization of constraint diagrams can be found in [8] . The language of spider diagrams [9, 10] forms a fragment of the constraint diagram language.  ... 
doi:10.1007/978-3-0348-0600-8_7 fatcat:5v2kvbnkj5f4fpjjb4ptbuzige

A diagrammatic reasoning system for the description logic

Frithjof Dau, Peter Eklund
2008 Journal of Visual Languages and Computing  
DLs correspond to decidable fragments of first order logic; their notation is in the style of symbolic, variable-free formulas.  ...  First, existing diagrammatic reasoning systems, namely spider-and constraint diagrams, as well as existential and conceptual graphs, are investigated to determine if they are compatible with DLs.  ...  In order to distinguish graphs from their diagrams, Peirce coined the term graph and graph replica, i.e., the above diagrams are different graph replicas of the same graph.  ... 
doi:10.1016/j.jvlc.2007.12.003 fatcat:krowcois6fcfrk2woevucrqm64

The expressiveness of spider diagrams augmented with constants

Gem Stapleton, John Taylor, Simon Thompson, John Howse
2009 Journal of Visual Languages and Computing  
We prove that this extended system is equivalent in expressive power to the language of spider diagrams without constants and, hence, equivalent to monadic first order logic with equality. r  ...  Several sound and complete spider diagram systems have been developed and it has been shown that they are equivalent in expressive power to monadic first order logic with equality.  ...  A formalization of constraint diagrams can be found in [8] . The language of spider diagrams [9, 10] forms a fragment of the constraint diagram language.  ... 
doi:10.1016/j.jvlc.2008.01.005 fatcat:kcnu44fn5bahpa6ej4piq5ibw4

Towards a Minimal Stabilizer ZX-calculus

Miriam Backens, Simon Perdrix, Quanlong Wang
2017 Logical Methods in Computer Science  
The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only if these two diagrams represent the same quantum evolution or  ...  Here, we show that most of the remaining rules of the language are indeed necessary. We do however leave as an open question the necessity of two rules.  ...  Thus, the above matrix expression is equal to the standard interpretation of a diagram consisting of green spiders, identities, and a swap.  ... 
doi:10.23638/lmcs-16(4:19)2020 fatcat:qg62mqnybrhpjl3yaldlsqgsbe

The Expressiveness of Spider Diagrams

G. Stapleton
2004 Journal of Logic and Computation  
In this paper we identify a well-known fragment of first-order predicate logic, that we call Å ÇÄ , equivalent in expressive power to the spider diagram language.  ...  Spider diagrams are a visual language for expressing logical statements.  ...  Thanks also to Andrew Fish, Jean Flower and Chris John for their comments on earlier drafts of this paper.  ... 
doi:10.1093/logcom/14.6.857 fatcat:4ibbmww2fzg5bb3b6rxcna6lky

Towards a Minimal Stabilizer ZX-calculus [article]

Miriam Backens, Simon Perdrix, Quanlong Wang
2020 arXiv   pre-print
The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only if these two diagrams represent the same quantum evolution or  ...  Here, we show that most of the remaining rules of the language are indeed necessary. We do however leave as an open question the necessity of two rules.  ...  Thus, the above matrix expression is equal to the standard interpretation of a diagram consisting of green spiders, identities, and a swap.  ... 
arXiv:1709.08903v6 fatcat:q2gm674snval7bkohtlxh2qayi

Speedith: A Reasoner for Spider Diagrams

Matej Urbas, Mateja Jamnik, Gem Stapleton
2015 Journal of Logic, Language and Information  
In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams.  ...  Speedith provides a way to input spider diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems.  ...  To identify corresponding regions, we need access to the missing zones and the empty zones in a unitary diagram, d. To simplify notation, we generalise the notion of an  ... 
doi:10.1007/s10849-015-9229-0 fatcat:vpwci6536jdvvbp653hsiim3y4

Universal MBQC with generalised parity-phase interactions and Pauli measurements

Aleks Kissinger, John van de Wetering
2019 Quantum  
However, when n>2, their behaviour diverges in two important ways.  ...  We furthermore show that for every n>2 this family is capable of producing all Clifford gates and all diagonal gates in the n-th level of the Clifford hierarchy.  ...  [26] ), any two diagrams of spiders with the same connectivity and ordering of inputs/outputs describe the same linear map.  ... 
doi:10.22331/q-2019-04-26-134 fatcat:syoopp2co5dsrmw4a6k37m5xry

Combined Transcript and Metabolite Analysis Reveals Genes Involved in Spider Mite Induced Volatile Formation in Cucumber Plants

P. Mercke
2004 Plant Physiology  
From the leaves of cucumber plants with and without spider mite infestation, two subtractive cDNA libraries were made that were enriched in cDNA fragments up-or down-regulated by spider mite infestation  ...  The resulting gene expression profiles were analyzed in combination with volatile production data in order to gain insight in the possible involvement of the studied genes in the synthesis of those volatiles  ...  Pearson correlation coefficient for the association of cDNA fragment to the volatile in that diagram is in brackets.  ... 
doi:10.1104/pp.104.048116 pmid:15310834 pmcid:PMC520772 fatcat:vtkexjk6tbfshlvt4i22xqjlh4

Egg Case Protein 3: A Constituent of Black Widow Spider Tubuliform Silk

Mikayla Shanafelt, Camille Larracas, Simmone Dyrness, Ryan Hekman, Coby La Mattina-Hawkins, Taylor Rabara, Wilson Wu, Craig A. Vierra
2021 Molecules  
Real-time reverse transcription–quantitative PCR analysis performed with different silk-producing glands revealed ECP3 mRNA is predominantly expressed within tubuliform glands of spiders.  ...  Spider silk has outstanding mechanical properties, rivaling some of the best materials on the planet.  ...  Lee, Jillian Lim, Ethan Nguyen, Jannet Nguyen, Jordan Nguyen, Patrick Pribadi, Phillip Pribadi, Angela Shu, and Jane Yu.  ... 
doi:10.3390/molecules26165088 pmid:34443676 pmcid:PMC8399404 fatcat:tudixpfj5bc65crcjblg7diwfa

Complete ZX-calculi for the stabiliser fragment in odd prime dimensions [article]

Robert I. Booth, Titouan Carette
2022 arXiv   pre-print
We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions.  ...  Adding a discard construction, we obtain a calculus complete for mixed state stabiliser quantum mechanics in odd prime dimensions, and this furthermore gives a complete axiomatisation for the related diagrammatic  ...  Acknowledgements The authors would like to thank Cole Comfort and Simon Perdrix for enlightening discussions.  ... 
arXiv:2204.12531v1 fatcat:2sfzzpovtfdtbakrzwjq5i2glm
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