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Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper…
Wave--particle duality is a cornerstone of quantum mechanics, traditionally formulated under definite causal order. We investigate how complementarity is modified when the temporal order of operations is coherently superposed, as in the…
Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from…
The article considers the quantitative assessment approach to the innovativeness of different objects. The proposed assessment model is based on the object data retrieval from various databases including the Internet. We present an object…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…
Logic-based models can be used to build verification tools for machine learning classifiers employed in the legal field. ML classifiers predict the outcomes of new cases based on previous ones, thereby performing a form of case-based…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
Quantifying the complexity of quantum states that possess intrinsic structure, such as symmetry or encoding, in a fair manner constitutes a core challenge in the benchmarking of quantum technologies. This paper introduces the…
Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
In quantitative program analysis, values are assigned to execution traces to represent a quality measure. Such analyses cover important applications, e.g. resource usage. Examining all traces is well known to be intractable and therefore…
Specification theories as a tool in model-driven development processes of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature, and therefore…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…