The present paper is a follow-up to the journal paper (Bra¨uner, 2014) which in turn is a revised and extended version of the conference paper (Bra¨uner, 2013). These papers were concerned with formalizations of the reasoning when giving correct responses to the psychological tests called the Sally-Anne task and the Smarties task, testing children’s capacity to ascribe false beliefs to others. In the present paper we give an analysis of what goes wrong when incorrect answers are given. Our analysis corroborates the claim that children under four and autistic children have difficulties shifting to a perspective different from their own.

The literature on first-order false-belief is extensive, but less isknown about the second-order case. The attainment of second-order false-belief mastery seems to mark a cognitively signifi-cant stage, but what is its status? Is it an example of complex-ity only development, or does it indicate that a more funda-mental conceptual change has taken place? In this paper weextend Bra ̈uner’s hybrid-logical analysis of first-order false-belief tasks (Bra ̈uner, 2014, 2015) to the second-order case,and argue that our analysis supports a version of the concep-tual change position.

Both first-order and second-order false-belief mastery are important in acquisition of Theory of Mind. Our logicalanalysis of second-order false-belief tasks shows that this sort of reasoning involves recursion. Language involves recursion aswell; recursive possessive and complements clauses are examples.Second-order social reasoning depends on both individual cognitive resources and immersion in a wide range of interactivecontexts. But since the ‘usual’ interactive contexts do not make the same sense to children with Autism Spectrum Disorder(ASD), it has been proposed that they use language as scaffolding in false-belief understanding.We hypothesize that competency in linguistic recursion predicts second-order false-belief mastery for children with ASD.We investigate this by training children with ASD to better comprehend and produce recursive possessive and complementclauses. We have developed and validated a tool to measure the recursion competency in the Danish language, and we applythis in a randomized controlled training study.

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.