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The Advent of Formal Diagrammatic Reasoning Systems [chapter]

Frithjof Dau
2009 Lecture Notes in Computer Science  
This paper discusses the evolution of formal diagrammatic logics, focusing on those systems which are based on Euler and Venn-Peirce diagrams, and Peirces existential graphs.  ...  Since then, certainly a growth in the research field of formal reasoning with diagrams can be witnessed.  ...  Acknowledgment The author wants to thank Gem Stapleton from the Visual Modelling Group for her valuable help and provision of diagrams.  ... 
doi:10.1007/978-3-642-01815-2_3 fatcat:qml7w6xy6ncv7fp7n4v4brlo2y

Heterogeneous Proofs: Spider Diagrams Meet Higher-Order Provers [chapter]

Matej Urbas, Mateja Jamnik
2011 Lecture Notes in Computer Science  
We provide a mechanisation of the theory of abstract spider diagrams and establish a formal link between diagrammatic concepts and the existing theories in Isabelle/HOL.  ...  We present an interactive heterogeneous theorem proving framework, which performs formal reasoning by arbitrarily mixing diagrammatic and sentential proof steps.  ...  Still, the intuitive nature of diagrams motivated the design of formal diagrammatic reasoning systems -for example, spider diagrams [6] and constraint diagrams [3] .  ... 
doi:10.1007/978-3-642-22863-6_29 fatcat:u5hbevxi7fagjcnk5sfcts4opu

Main Problems of Diagrammatic Reasoning. Part I: The generalization problem

Zenon Kulpa
2008 Foundations of Science  
that diagrammatic reasoning lacks the rigour necessary for mathematical reasoning.  ...  Some of the methods are adapted from similar methods used in reasoning with formulae, several other problems constitute new, specifically diagrammatic ways of reliable reasoning.  ...  Acknowledgements The research leading to this paper was partially supported by the Research Project No. 5 T07F 002 25 (for the years [2003][2004][2005][2006], granted by KBN (State Committee for Scientific  ... 
doi:10.1007/s10699-008-9148-5 fatcat:5ztplrlpzjcpxnqnn75737ooni

Vivid: A framework for heterogeneous problem solving

Konstantine Arkoudas, Selmer Bringsjord
2009 Artificial Intelligence  
We extend the assumption-base semantics of DPLs to accommodate diagrammatic reasoning by introducing general inference mechanisms for the valid extraction of information from diagrams, and for the incorporation  ...  We present novel formal structures, called named system states, that are specifically designed for modeling potentially underdetermined diagrams.  ...  Our focus, by contrast, has been precisely the modeling of the reasoning itself-the formal modeling of what "the reasoner does in the course of the reasoning."  ... 
doi:10.1016/j.artint.2009.06.002 fatcat:bcbqe3ldj5eexjz7w74kmhxs6e

The Epistemological Import of Euclidean Diagrams (in a non-Euclidean world)

Daniele Molinini
2016 Kairos: Journal of Philosophy & Science  
I shall claim that, although the world we live in is not Euclidean, Euclidean diagrams permit to obtain knowledge of the world through a specific mechanism of inference I shall call inheritance.  ...  In this paper I concentrate on Euclidean diagrams, namely on those diagrams that are licensed by the rules of Euclid's plane geometry.  ...  And this despite the advent of more sophisticated, non-Euclidean, mathematical concepts and formal systems.  ... 
doi:10.1515/kjps-2016-0012 fatcat:gsusn5ikzzbold4fsev3mhjupi

Zen and the art of formalisation

ANDREA ASPERTI, JEREMY AVIGAD
2011 Mathematical Structures in Computer Science  
The problem is, rather, that ordinary mathematical proofs rely on patterns of reasoning-say, combinatorial, geometric, or diagrammatic-that are often difficult to analyze and explain in terms of formal  ...  With the advent of interactive proof assistants, we are now beginning to develop substantial corpora of machine-readable mathematics.  ... 
doi:10.1017/s0960129511000065 fatcat:wl4eh6fdjjeblpbi3xobqnpvzq

Typal and typological reasoning: a diagrammatic practice of architecture

Sam Jacoby
2015 Journal of Architecture  
Clarifying the concept of type as emerging in parallel with ideas of abstraction and diagrammatic reasoning reveals a richer set of connected problems deriving from architectural practice, pedagogy, and  ...  Although not prescriptive in a formal sense, they are concerned with a rational synthesis of form by thinking through conceptual and diagrammatic organisation.  ...  To clarify the concept of type as emerging in parallel with ideas of abstraction and diagrammatic reasoning reveals a richer set of connected problems that derive from architectural practice, pedagogy,  ... 
doi:10.1080/13602365.2015.1116104 fatcat:7zqsodhlerbdzdk5etf5gkqkta

Speedith: A Reasoner for Spider Diagrams

Matej Urbas, Mateja Jamnik, Gem Stapleton
2015 Journal of Logic, Language and Information  
This allows for other systems to access diagrammatic reasoning via Speedith, as well as a formal verification of diagrammatic proof steps within standard sentential proof assistants.  ...  We describe the general structure of Speedith, the diagrammatic language, the automatic mechanism that draws the diagrams when inference rules are applied on them, and how formal diagrammatic proofs are  ...  Acknowledgments We thank Jean Flower for her help with iCircles extension, and Charlie Bashford-Chuchla for his implementation of SpiderDrawer as part of his MPhil project in the University of Cambridge  ... 
doi:10.1007/s10849-015-9229-0 fatcat:vpwci6536jdvvbp653hsiim3y4

Relational logics and diagrams: 'No-scale conditions'
Relacione logike i dijagrami - stanja bez razmere (nemetrička stanja)

Dragana Ćirić
2016 SAJ. Serbian architectural journal  
, ending with some of the relational diagrammatic and topological ways of architectural data-processing outside of the spatial constraints and parameters - all through diagrams as ultimate tools of relational  ...  nonlinearity and complexity by symmetry-breakings within non-metric systems.  ...  What is diagrammatic reasoning?  ... 
doi:10.5937/saj1603388q fatcat:nofua5qouvf3nc6qmzou3b7qv4

EVALUATION ISSUES FOR VISUAL PROGRAMMING LANGUAGES [chapter]

TIM MENZIES
2002 Handbook of Software Engineering and Knowledge Engineering  
If we extend the concept of VP systems to diagrammatic reasoning in general, then we can make a case that VP has some such benefits.  ...  Executable visual representations, however, have only arisen with the advent of the computer.  ...  Communications of the ACM Proceedings of the AAAI Symposium on Diagrammatic Reasoning Stanford University, March Proceedings of the AAAI Symposium on Diagrammatic Reasoning Stanford University, March  ... 
doi:10.1142/9789812389701_0005 fatcat:4qc5lylpmvayhdnlx2aoc4yyga

What are the fundamental structures of concurrency? We still don't know! [article]

Samson Abramsky
2014 arXiv   pre-print
Process algebra has been successful in many ways; but we don't yet see the lineaments of a fundamental theory. Some fleeting glimpses are sought from Petri Nets, physics and geometry.  ...  Moreover, the need to recognize the spatial structure of distributed systems has become apparent, and is made explicit in formalisms such as the Ambient calculus, and Milner's bigraphs.  ...  Consider obvious exemplars such as • Process Calculi • Type Systems • Model-checking It is not the case that there is a single agreed model, notation, formalism, tool or language in any of the above areas  ... 
arXiv:1401.4973v1 fatcat:xpfawrxcfnfbxomlhrd3vgh5ii

Strangeness production via electromagnetic probes: 40 years later [article]

Bijan Saghai
2003 arXiv   pre-print
The preliminary results of this work are reported here.  ...  A brief review of the associated strangeness electromagnetic production is presented.  ...  The couplings extracted within the coupled-channel formalisms can then be embodied in the isobaric approaches, including a reasonable number of resonances, to produce the needed elementary operators and  ... 
arXiv:nucl-th/0310025v1 fatcat:4fkdktsiarbmphkyijlp75yoeq

Compositionality as we see it, everywhere around us [article]

Bob Coecke
2021 arXiv   pre-print
The most established conception is usually attributed to Frege, and is characterised by a bottom-up flow of meanings: the meaning of the whole can be derived from the meanings of the parts, and how these  ...  At this point we only put forward the intuitive and/or restricted formal definitions, and leave a fully comprehensive definition to future collaborative work.  ...  At the time that this picture was taken, Vincent was still playing with teddy bears. Stephen Clark, Amar Hadzihasanovic, Arkady Plotnitsky, Ilyas Khan and Ian Durham also provided feed-back.  ... 
arXiv:2110.05327v2 fatcat:hrc2las5zvghjhhv3r2j4dlsty

What are the Fundamental Structures of Concurrency?

Samson Abramsky
2006 Electronical Notes in Theoretical Computer Science  
Process algebra has been successful in many ways; but we don't yet see the lineaments of a fundamental theory. Some fleeting glimpses are sought from Petri Nets, physics and geometry.  ...  Moreover, the need to recognize the spatial structure of distributed systems has become apparent, and is made explicit in formalisms such as the Ambient calculus, and Milner's bigraphs.  ...  There is no doubt that the advent of algebraic process calculi marked a decisive advance in concurrency theory, in particular in the use of compositional algebraic methods for the description of complex  ... 
doi:10.1016/j.entcs.2005.12.075 fatcat:jwe2dlccebe6rguycdtg2gtqwi

Scientific Discovery With Law-Encoding Diagrams

Peter C.-H. Cheng
1996 Creativity Research Journal  
Previous work on the computational modelling of diagrammatic law induction is reinterpreted in terms of the search for diagrammatic constraints of LEDs.  ...  A LED is a representation that correctly encodes the underlying relations of a law, or a system of simultaneous laws, in the structure of a diagram by the means of geometric, topological and spatial constraints  ...  Nomograms are a class of diagrammatic representations that were used for computing quantitative solutions to equations before the advent of electronic calculators.  ... 
doi:10.1080/10400419.1996.9651169 fatcat:5gcrxgdc2febrbmybldmavfzeq
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