A Framework for Heterogeneous Reasoning in Formal and Informal Domains

Urbas, Matej; Jamnik, Mateja

doi:10.1007/978-3-662-44043-8_28

Cited by 14 publications

(11 citation statements)

References 9 publications

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“…Various formalisations of specific reasoning systems using a single kind of representation have been implemented, including first order [16,15], higher order [11,21], diagrammatic [27,13,28], among many others. A few heterogeneous reasoning systems that integrate multiple representations have also been built [2,26], as well as some tools for re-representing problems and knowledge across and within systems [19,12,23]. Many systems designed for numerical, algebraic, and geometric computing include tools for representing data in various ways (graphs, plots, figures, diagrams, etc.)…”

Section: The Role Of Representation In Reasoningmentioning

confidence: 99%

Inspection and Selection of Representations

Raggi

Stockdill

Jamnik

et al. 2019

Lecture Notes in Computer Science

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We present a novel framework for inspecting representations and encoding their formal properties. This enables us to assess and compare the informational and cognitive value of different representations for reasoning. The purpose of our framework is to automate the process of representation selection, taking into account the candidate representation's match to the problem at hand and to the user's specific cognitive profile. This requires a language for talking about representations, and methods for analysing their relative advantages. This foundational work is first to devise a computational end-to-end framework where problems, representations, and user's profiles can be described and analysed. As AI systems become ubiquitous, it is important for them to be more compatible with human reasoning, and our framework enables just that.

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Section: The Role Of Representation In Reasoningmentioning

confidence: 99%

Inspection and Selection of Representations

Raggi

Stockdill

Jamnik

et al. 2019

Lecture Notes in Computer Science

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“…Other techniques draw 3D Euler diagrams [FSR14] or Euler diagrams for reasoning [Sta05] (e.g. spider diagrams [HST05]), specifying constraints [SD08], defining ontologies [HSTC11, OHS*09] and proving theorems [UJ14, UJ12, UJSF12].…”

Section: A Survey Of Set Visualization Techniquesmentioning

confidence: 99%

The State‐of‐the‐Art of Set Visualization

Alsallakh

Micallef

Aigner

et al. 2015

Computer Graphics Forum

111

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Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net.

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“…It is also possible to import sentential formulae into Speedith by translating them into spider diagrams. This pluggable feature of Speedith was exploited via the MixR framework [32] where Speedith was integrated with a sentential theorem prover Isabelle to result in the Diabelli [31] heterogeneous reasoning system (i.e., a mixture of diagrammatic and sentential inference steps make the statements and the proof of a theorem) -for more information, see [32].…”

Section: Architecture and Implementationmentioning

confidence: 99%

“…An advantage of Speedith's abstract representation is the ease of transformation of spider diagrams into sentential first-order logic (for more information, see [32]). This representation is also designed with the aim for quick manipulations of spider diagrams through the application of inference rules (to make reasoning as efficient as possible).…”

Section: Definition 12mentioning

confidence: 99%

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Speedith: A Reasoner for Spider Diagrams

Urbas

Jamnik

2015

J of Log Lang and Inf

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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. Speedith's inference rules are sound and complete, extending previous research by including all the classical logic connectives. In addition to being a stand-alone proof system, Speedith is also designed as a program that plugs into existing general purpose theorem provers. 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 constructed.

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A Framework for Heterogeneous Reasoning in Formal and Informal Domains

Cited by 14 publications

References 9 publications

Inspection and Selection of Representations

Inspection and Selection of Representations

The State‐of‐the‐Art of Set Visualization

Speedith: A Reasoner for Spider Diagrams

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