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Diagrammatic Reasoning in Separation Logic [chapter]

M. Ridsdale, M. Jamnik, N. Benton, J. Berdine
Lecture Notes in Computer Science  
Rather than proving program specifications symbolically, the hope is to model more closely human diagrammatic reasoning, and to perform automated diagrammatic reasoning in separation logic.  ...  A new method of reasoning about simple imperative programs in separation logic is proposed.  ...  The ideas on diagrammatic reasoning are drawn from [1] , which is on diagrammatic theorem proving in arithmetic; we also draw on ideas from [2] , which is on symbolic automated theorem proving in separation  ... 
doi:10.1007/978-3-540-87730-1_50 fatcat:adrkefds5vaxpi6s5k7zc4cway

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.  ...  The diagrammatic part of the framework is not formalised within the logic of the sentential reasoner. Therefore, the diagrammatic and sentential components remain logically separated.  ... 
doi:10.1007/978-3-642-22863-6_29 fatcat:u5hbevxi7fagjcnk5sfcts4opu

Diabelli: A Heterogeneous Proof System [chapter]

Matej Urbas, Mateja Jamnik
2012 Lecture Notes in Computer Science  
We present Diabelli, a formal reasoning system that enables users to construct so-called heterogeneous proofs that intermix sentential formulae with diagrams.  ...  The Diagrammatic Reasoner Spider Diagrams. The language of spider diagrams is used in Speedith, which constitutes the diagrammatic reasoning part of our heterogeneous system.  ...  A screenshot of a heterogeneous proof in Diabelli execute them. The results are returned back to I3P, which displays them in a separate result window.  ... 
doi:10.1007/978-3-642-31365-3_44 fatcat:ybufjsgvv5epllwm7n2psgd6fa

Visual Reasoning about Ontologies

John Howse, Gem Stapleton, Ian Oliver
2010 International Semantic Web Conference  
We explore a diagrammatic logic suitable for specifying ontologies using a case study. Diagrammatic reasoning is used to establish consequences of the ontology.  ...  This is, perhaps, a primary advantage of reasoning with a well-designed diagrammatic logic. Conclusion. We have demonstrated how to reason with concept diagrams.  ...  Using diagrammatic notations for reasoning, in addition to specification, can bring benefits.  ... 
dblp:conf/semweb/HowseSO10 fatcat:4cbvgxhkxjexbdir4ncjvtos2y

Diagrammatic Evaluation of Visual Mathematical Notations [chapter]

Bernd Meyer
2002 Diagrammatic Representation and Reasoning  
For reasoning about certain types of diagrams, however, formalizing a notion of change is inevitable.  ...  Formal specification techniques for diagrammatic or visual languages have previously mainly been targeted towards static diagrammatic languages.  ...  Acknowledgments The author gratefully acknowledges discussions with Kim Marriott during a stay at Monash University in which many ideas on diagram formalization were either born or substantially refined  ... 
doi:10.1007/978-1-4471-0109-3_15 fatcat:2667dsfx2rds3cep3tv7kki4ju

Shape Perception in Chemistry

Janna Hastings, Colin R. Batchelor, Mitsuhiro Okada
2013 Interdisciplinary Workshop The Shape of Things  
Algorithmic and logic-based approaches to representation and automated reasoning with chemical structures are able to efficiently compute certain features, such as detecting presence of specific functional  ...  We conduct a study in which we vary the diagrammatic representation from the canonical diagrammatic standard of the chemicals, and evaluate speed of human determination of chemical class.  ...  Such hybrid systems have been advanced in other domains. For example, the Vivid system offers some diagrammatic reasoning capability alongside logical reasoning capability [1] .  ... 
dblp:conf/shapes/HastingsBO13 fatcat:jl3au53n4raihan7wlddfztbdy

"... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning"

Michael Hoffmann
2018 Eurasia Journal of Mathematics, Science and Technology Education  
Peirce developed two different concepts-"abduction" and "diagrammatic reasoning"-that are interesting for theories of creativity in mathematics, the sciences, and in learning.  ...  In this contribution, I start from a remark by Peirce claiming that diagrammatic reasoning might somehow be the foundation of abduction.  ...  We know already that for Peirce, "All necessary reasoning is diagrammatic," but such necessary reasoning is not only present in logic but also in mathematics.  ... 
doi:10.29333/ejmste/92553 fatcat:67zacp4ivzhh7jetagcs7qpgmm

What is Diagrammatic Reasoning in Mathematics?

Michał Sochański
2018 Logic and Logical Philosophy  
Main differences between those types of reasoning are also hinted at. A distinction between visual (diagrammatic) reasoning and visual (diagrammatic) thinking is also considered.  ...  In this paper it is proposed to distinguish between several ways of using visualization or diagrams in mathematics, each of which could be connected with a different concept of diagrammatic/visual reasoning  ...  Rather, diagrams are treated as separate symbols themselves.  ... 
doi:10.12775/llp.2018.001 fatcat:lepe6ivctvdh5gj3p4wj7rpic4

Speedith: A Diagrammatic Reasoner for Spider Diagrams [chapter]

Matej Urbas, Mateja Jamnik, Gem Stapleton, Jean Flower
2012 Lecture Notes in Computer Science  
In this paper, we introduce Speedith which is a diagrammatic theorem prover for the language of spider diagrams.  ...  Spider diagrams are a well-known logic for which there is a sound and complete set of inference rules.  ...  It is used when verifying particular steps in the diagrammatic proof, or verifying properties about spider-diagrammatic formulae in a sentential reasoner.  ... 
doi:10.1007/978-3-642-31223-6_19 fatcat:kcavkfwnzbearnosffi2fj4nt4

A Proposal for Automating Diagrammatic Reasoning in Continuous Domains [chapter]

Daniel Winterstein, Alan Bundy, Mateja Jamnik
2000 Lecture Notes in Computer Science  
This paper presents one approach to the formalisation of diagrammatic proofs as an alternative to algebraic logic.  ...  This approach involves creating a diagrammatic theory. The method is justified formally by (a) a diagrammatic axiomatisation, and (b) an appeal to analysis, viewing the diagram as an object in Ê 2 .  ...  It combines a first order logic prover with a visual representation for reasoning in a blocks world domain [2] .  ... 
doi:10.1007/3-540-44590-0_26 fatcat:mbnvzipoujernjnlc7todptx2m

Tactical Diagrammatic Reasoning

Sven Linker, Jim Burton, Mateja Jamnik
2017 Electronic Proceedings in Theoretical Computer Science  
Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins.  ...  In this paper we take an interactive proof assistant for Euler diagrams, Speedith, and add tactics to its reasoning engine, providing a level of automation in the construction of proofs.  ...  Tactical Diagrammatic Reasoning Background Diagrammatic logics such as Euler diagrams have a number of striking differences from sentential logics.  ... 
doi:10.4204/eptcs.239.3 fatcat:nvd7gb3ti5ag3p32zy5t22iv3i

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.  ...  In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams.  ...  Similar notions of corresponding sub-regions and super-regions will also be defined in this section.  ... 
doi:10.1007/s10849-015-9229-0 fatcat:vpwci6536jdvvbp653hsiim3y4

Peirce's diagrammatic reasoning and the cinema: Image, diagram, and narrative in The Shape of Water

Yunhee Lee, Paul Cobley
2020 Semiotica: Journal of the International Association for Semiotic Studies  
The article outlines two kinds of diagrammatic reasoning emphasized by Peirce: corollarial deduction in which the image is 'literally seen' and the reasoning steps are manifest in its conclusion; and theorematic  ...  Demonstrating the breadth of diagrammatic reasoning with reference to the 2018 film, The Shape of Water, the article seeks to explore how allegory and diagram are mutually cooperative, based on three ontological  ...  Peirce's diagrammatic reasoning and the cinema  ... 
doi:10.1515/sem-2019-0025 fatcat:6wx4ksgdtzfq7a32rikqc6ujce

The Semiotics of Spider Diagrams

Jim Burton, John Howse
2017 Logica Universalis  
Our hope is that this analysis may be of interest beyond those readers particularly interested in spider diagrams, and act as a case study in deconstructing a simple visual logic.  ...  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  ...  In zone A ∩ B, s and t are separated in D 1 and connected by a strand in D 2 ; hence in D they are separated.  ... 
doi:10.1007/s11787-017-0167-2 fatcat:j4ywlgct5bctllkv6hxcs7pjqy

Picturing Problems: Solving Logic Puzzles Diagrammatically

John Howse, Gem Stapleton, Jim Burton, Andrew Blake
2018 Diagrams  
Diagrammatic logics have been shown to help people to understand and reason about logical information.  ...  Furthermore, we reason with the diagrammatic representation both syntactically and semantically until we reach a solution.  ...  There is a widespread belief that the use of diagrammatic logics, such as Euler diagrams, is helpful in allowing people to understand and reason about logical information.  ... 
dblp:conf/diagrams/HowseSB018 fatcat:bmdamenoobdyldmnuutor5xdma
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