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Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction in the construction of proofs and of providing explanations of solutions expressed in the proofs remain to be addressed. 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. By adding tactics to Speediths repertoire of inferences, we ease the interaction between the user and the system and capture a higher level explanation of the essence of the proof. We analysed the design options for tactics by using metrics which relate to human readability, such as the number of inferences and the amount of clutter present in diagrams. Thus, in contrast to the normal case with sentential tactics, our tactics are designed to not only prove the theorem, but also to support explanation.
Diagrammatic logics were introduced in 2002, with emphasis on the notions of specifications and models. In this paper we improve the description of the inference process, which is seen as a Yoneda functor on a bicategory of fractions. A diagrammatic
Learning to solve diagrammatic reasoning (DR) can be a challenging but interesting problem to the computer vision research community. It is believed that next generation pattern recognition applications should be able to simulate human brain to under
This paper is a submission to the contest: How to combine logics? at the World Congress and School on Universal Logic III, 2010. We claim that combining things, whatever these things are, is made easier if these things can be seen as the objects of a
Abstract reasoning, particularly in the visual domain, is a complex human ability, but it remains a challenging problem for artificial neural learning systems. In this work we propose MXGNet, a multilayer graph neural network for multi-panel diagramm
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is considera