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We propose a qualitative representation for handling shape change and object division. We model the shape of a smooth curve in a two-dimensional plane together with its temporal change, using curvature extrema. The representation is based on Process-Grammar, which gives a causal account for each shape change. We introduce several rewriting rules to handle object division, that consist of making a tangent point, reconstruction, and separation. On the treatment of the division process, the expression can clarify the relative locations of multiple objects. We show formalization and application to represent a sequence of shape changes frequently observed in an organogenesis process.

We propose a qualitative representation for handling shape change and object division. We model the shape of a smooth curve in a two-dimensional plane together with its temporal change, using curvature extrema. The representation is based on Process-Grammar, which gives a causal account for each shape change. We introduce several rewriting rules to handle object division, that consist of making a tangent point, reconstruction, and separation. On the treatment of the division process, the expression can clarify the relative locations of multiple objects. We show formalization and application to represent a sequence of shape changes frequently observed in an organogenesis process.

In this paper, we propose a new method for computing general allocators directly from completeness conditions. A general allocator is an abstraction of all complete labelings for an argumentation framework. Any complete labeling is obtained from a general allocator by assigning logical constants to variables. We proved the existence of the general allocators in our previous work. However, the construction requires us to enumerate all complete labelings for the framework, which makes the computation prohibitively slow. The method proposed in this paper enables us to compute general allocators without enumerating complete labelings. It also provides the solutions of local allocation that yield semantics for subsets of the framework. We demonstrate two applications of general allocators, stability, and a new concept for frameworks, termed arity. Moreover, the method, including local allocation, is applicable to broad extensions of frameworks, such as argumentation frameworks with set-attacks, bipolar argumentation frameworks, and abstract dialectical frameworks.

We prove the 169 compositions of time interval relations. The proof is first-order and inferred from an axiomatic system on time intervals. We show a general proof template that can alleviate the manual proof with Isar., Comment: Proofs available for checking: https://www.isa-afp.org/entries/Allen_Calculus.html