Diagrammatic Reasoning in

@inproceedings{Frixione2001DiagrammaticRI,
  title={Diagrammatic Reasoning in},
  author={Marcello Frixione and Gianni Viardo Vercelli and Renato Zaccaria},
  year={2001}
}
Danielle Macbeth In Part III of his 1879 logic1 Frege proves a theorem in the theory of sequences on the basis of four definitions. He claims in Grundlagen that this proof, despite being strictly deductive, constitutes a real extension of our knowledge, that it is ampliative rather than merely explicative: “From this proof it can be seen that propositions that extend our knowledge can have analytic judgments for their content”.2 Frege furthermore connects this idea of ampliative deductive… 

JAMIE TAPPENDEN PROOF STYLE AND UNDERSTANDING IN MATHEMATICS I : VISUALIZATION , UNIFICATION AND AXIOM CHOICE 0 To the memory of

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with

Constructing internal diagrammatic proofs from external logic diagrams

It is argued that internal manipulations of dia- grams, or what the authors call internal constructions of diagrammatic proofs, actually exist, and that such constructions are naturally triggered even for users without explicit prior knowledge of their inference rules or strategies.

Interpreting logic diagrams: a comparison of two formulations of diagrammatic representations

The present paper investigates the cog- nitive processes of interpreting diagrammatic representations underlying deductive reasoning, combining the insights from both logical and cognitive studies of diagrams.

“ Linguistic ” vs . “ Non-Linguistic ” Representations : On the Nature of the Theoretical Constructs of the Cognitive Sciences

Within the field of the cognitive sciences (CSs), frequently happened that some form of “linguistic” representations (symbols, propositional representations, and so on) have been opposed to

Can Diagrams Have Epistemic Value? The Case of Euclid

This chapter discusses the problem of generality: how reasoning with a single diagram can justify knowledge of a general mathematical claim.

A Theorem Prover for a Diagrammatic Blocks World

This paper summarizes the design and implementation of a diagrammatic theorem prover and shows that a well-formed syntax and semantic can be defined for this system, and defines valid rules of inference with which to give proofs in the system.

Using Venn Diagrams to Perform Logic Reasoning: An Algorithm for Automating the Syllogistic Reasoning of Categorical Statements

  • R. Nakatsu
  • Computer Science
    Int. J. Intell. Syst.
  • 2014
The Venn diagramming algorithm for syllogistic reasoning is extended to allow for more than three sets of information at a time and makes use of tables, which is also very intuitive and highly visual.

A Diagrammatic Inter-Lingua for Planning Domain Descriptions

A theoretical analysis shows how the representation can be easily encoded using formal languages, and demonstrates that setGraphs are at least as expressive as a standard modern propositional planning domain description language.

A Compositional Model of Consciousness Based on Consciousness-Only

This work sets up a framework which naturally subsumes one of the main features of consciousness that is characterized as being other-dependent by defining a compact closed category where morphisms represent conscious processes.

Multiple Levels of Heuristic Reasoning Processes in Scientific Model Construction

Science historians have recognized the importance of heuristic reasoning strategies for constructing theories, but their extent and degree of organization are still poorly understood. This paper

References

SHOWING 1-10 OF 55 REFERENCES

Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems

When I started out as a newly hatched PhD student, one of the first articles I read and understood was Ray Reiter’s classic article on default logic, and I became fascinated by both default logic and, more generally, non-monotonic logics.

Why a Diagram is (Sometimes) Worth Ten Thousand Words

Some Pictures Are Worth 2 א 0 Sentences

According to the cliché, a picture is worth a thousand words. But this is a ca-nard, for it vastly underestimates the expressive power of many pictures and diagrams. Even a simple map, such as the

Qualitative Spatial Reasoning: Framework and Frontiers

Spatial reasoning is a diverse topic; what might different spatial tasks have in common? One task where substantial progress has been made is qualitative spatial reasoning about motion. Unlike

Qualitative Spatial Reasoning: The Clock Project

Conceptual spaces - the geometry of thought

Peter Gardenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level and shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics.

Realization of a geometry theorem proving machine

The technique of heuristic programming is under detailed investigation as a means to the end of applying large-scale digital computers to the solution of a difficult class of problems currently considered to be beyond their capabilities; namely those problems that seem to require the agent of human intelligence and ingenuity for their solution.

Reasoning with Diagrammatic Representations: A Report on the Spring Symposium

A framework for thinking about the issues that were the focus of the spring 1992 symposium on diagrammatic representations in reasoning and problem solving is developed and it is anticipated that traditional symbolic representations will increasingly be combined with iconic representations in future AI research and technology.

Problem-Solving with Diagrammatic Representations

  • B. Funt
  • Computer Science
    Artif. Intell.
  • 1980

Analogical Representations of Naive Physics

...