This workshop explores the influence of AI systems on human decision-making - algorithmic authority - and the broader concept of technology dominance, which includes both positive and negative impacts of AI reliance. Drawing from diverse fields such as Human-AI Interaction, Sociology, Epistemology, and Cognitive Science, the workshop will discuss theoretical foundations, empirical studies, and design implications of AI’s role in shaping human judgment and behavior. The objectives are to examine in-depth the concepts of algorithmic authority and technology dominance, and identify metrics for their assessment. The workshop aims to foster interdisciplinary collaboration and produce practical design principles that help to counter risks associated to AI technology dominance and thus foster a responsible use of AI systems.

Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate . In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.

A landmark result in the study of logics for formal verification is Janin and Walukiewicz’s theorem, stating that the modal μ-calculus (μML) is equivalent modulo bisimilarity to standard monadic second-order logic (here abbreviated as SMSO) over the class of labelled transition systems (LTSs for short). Our work proves two results of the same kind, one for the alternation-free or noetherian fragment μ N ML of μML on the modal side and one for WMSO, weak monadic second-order logic, on the second-order side. In the setting of binary trees, with explicit functions accessing the left and right successor of a node, it was known that WMSO is equivalent to the appropriate version of alternation-free μ-calculus. Our analysis shows that the picture changes radically once we consider, as Janin and Walukiewicz did, the standard modal μ-calculus, interpreted over arbitrary LTSs. The first theorem that we prove is that, over LTSs, μ N ML is equivalent modulo bisimilarity to noetherian MSO (NMSO), a newly introduced variant of SMSO where second-order quantification ranges over “conversely well-founded” subsets only. Our second theorem starts from WMSO and proves it equivalent modulo bisimilarity to a fragment of μ N ML defined by a notion of continuity. Analogously to Janin and Walukiewicz’s result, our proofs are automata-theoretic in nature: As another contribution, we introduce classes of parity automata characterising the expressiveness of WMSO and NMSO (on tree models) and of μ C ML and μ N ML (for all transition systems).

For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a nondeterministic, alternating, or weak alternating parity automaton. These questions are known as, respectively, the nondeterministic, alternating, and weak Rabin-Mostowski index problems. Whether they can be answered effectively is a long-standing open problem, solved so far only for languages recognizable by deterministic automata (the alternating variant trivializes). We investigate a wider class of regular languages, recognizable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. Game automata are known to recognize languages arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is, the alternating index problem does not trivialize anymore. Our main contribution is that all three index problems are decidable for languages recognizable by game automata. Additionally, we show that it is decidable whether a given regular language can be recognized by a game automaton.

For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognise this language with a non-deterministic or alternating parity automaton. These questions are known as, respectively, the non-deterministic and the alternating Rabin-Mostowski index problems. Whether they can be answered effectively is a long-standing open problem, solved so far only for languages recognisable by deterministic automata (the alternating variant trivialises). We investigate a wider class of regular languages, recognisable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. Game automata are known to recognise languages arbitrarily high in the alternating Rabin-Mostowski index hierarchy, i.e., the alternating index problem does not trivialise any more. Our main contribution is that both index problems are decidable for languages recognisable by game automata. Additionally, we show that it is decidable whether a given regular language can be recognised by a game automaton.

We provide a characterization theorem, in the style of van Benthem and Janin-Walukiewicz, for the alternation-free fragment of the modal μ-calculus. For this purpose we introduce a variant of standard monadic second-order logic (MSO), which we call well-founded monadic second-order logic (WFMSO). When interpreted in a tree model, the second-order quantifiers of WFMSO range over subsets of conversely well-founded subtrees. The first main result of the paper states that the expressive power of WFMSO over trees exactly corresponds to that of weak MSO-automata. Using this automata-theoretic characterization, we then show that, over the class of all transition structures, the bisimulation-invariant fragment of WFMSO is the alternation-free fragment of the modal μ-calculus. As a corollary, we find that the logics WFMSO and WMSO (weak monadic second-order logic, where second-order quantification concerns finite subsets), are incomparable in expressive power.

Alternating automata on infinite trees induce operations on languages which do not preserve natural equivalence relations, like having the same Mostowski--Rabin index, the same Borel rank, or being continuously reducible to each other (Wadge equivalence). In order to prevent this, alternation needs to be restricted to the choice of direction in the tree. For weak alternating automata with restricted alternation a small set of computable operations generates all definable operations, which implies that the Wadge degree of a given automaton is computable. The weak index and the Borel rank coincide, and are computable. An equivalent automaton of minimal index can be computed in polynomial time (if the productive states of the automaton are given).

Recently, Miko{\l}aj Boja{\'n}czyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving manyof its usual properties. This new class can be seen as a different way of generalising the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity.It is proved that up to Wadge equivalence the classes coincide. Moreover, when restricted to $\mathbf{\Delta}^0_2$-languages, the classes contain virtually the same languages. On the other hand, separating examples of arbitrary complexity exceeding $\mathbf{\Delta}^0_2$ are constructed.

Abstract We study the strictness of the modalμ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternation-free fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for reflexive systems the same results holds for finite models.