This paper surveys a new perspective on tree automata and Monadic second-order logic (MSO) on infinite trees. We show that the operations on tree automata used in the translations of MSO-formulae to automata underlying Rabin’s Tree Theorem (the decidability of MSO) correspond to the connectives of Intuitionistic Multiplicative Exponential Linear Logic (IMELL). Namely, we equip a variant of usual alternating tree automata (that we call uniform tree automata) with a fibered monoidal-closed structure which in particular handles a linear complementation of alternating automata. Moreover, this monoidal structure is actually Cartesian on non-deterministic automata, and an adaptation of a usual construction for the simulation of alternating automata by non-deterministic ones satisfies the deduction rules of the !(–) exponential modality of IMELL. (But this operation is unfortunately not a functor because it does not preserve composition.) Our model of IMLL consists in categories of games which are based on usual categories of two-player linear sequential games called simple games, and which generalize usual acceptance games of tree automata. This model provides a realizability semantics, along the lines of Curry–Howard proofs-as-programs correspondence, of a linear constructive deduction system for tree automata. This realizability semantics, which can be summarized with the slogan “automata as objects, strategies as morphisms,” satisfies an expected property of witness extraction from proofs of existential statements. Moreover, it makes it possible to combine realizers produced as interpretations of proofs with strategies witnessing (non-)emptiness of tree automata.

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.

Similar peers are more likely to become friends, but it remains unclear how the combination of multiple characteristics, known as multidimensional similarity, influences friendships. This study aimed to investigate whether similarity in gender (attribute) and bullying or victimization (network position) contributes to friendships. The school-level networks of friendships and victim-bully relationships in 17 Dutch elementary schools (2,130 students) were examined using multiplex longitudinal social network models (RSiena). The results showed that friendships were more likely to occur between same-gender peers and between bullies sharing their targets of victimization. Multidimensional similarity (similarities in gender as well as bullying) increased the likelihood of friendships for same-gender bullies targeting the same victims, but not for same-gender victims sharing bullies. The findings underline the importance of unraveling the interplay between different dimensions of similarity for children’s relationships and surpass unidimensional similarity based on single attributes.

The computer aided internal optimisation (CAIO) method produces an optimised fibre layout for parts made from fibre-reinforced plastics (FRP), starting from an initial shell geometry and a given load case. Its main principle is iterative reduction of shear stresses by aligning fibre main axes with principal normal stress trajectories. Previous contributions, ranging from CAIO’s introduction over testing to extensions towards multi-layer FRP laminates, highlighted its lightweight design potential. For its application to laminate design approaches, alterations have been proposed; however, questions remain open. These questions include which convergence criteria to use, how to handle ambiguous principle normal stress trajectories, influence of using multi-layer CAIO optimisation instead of the initial single-layer CAIO and how dire consequences of slightly deviating fibre orientations from the optimised trajectories are. These challenges are discussed in depth and guidelines are given. This paper is an enhanced version of a distinguished contribution at the first symposium ‘Lightweight Design in Product Development’, Zurich (June 14–15, 2018).