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Large language models are emerging as scientific assistants, but evaluating their ability to reason from empirical data remains challenging. Benchmarks derived from published studies and human annotations inherit publication bias,…
For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
In this paper, we revisit Moggi's celebrated calculus of computational effects from the perspective of logic of monoidal action (actegory). Our development takes the following steps. Firstly, we perform proof-theoretic reconstruction of…
The assessment of process mining techniques using real-life data is often compromised by the lack of ground truth knowledge, the presence of non-essential outliers in system behavior and recording errors in event logs. Using synthetically…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
This paper deals with belief base revision that is a form of belief change consisting of the incorporation of new facts into an agent's beliefs represented by a finite set of propositional formulas. In the aim to guarantee more reliability…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…
Process mining is a technique that performs an automatic analysis of business processes from a log of events with the promise of understanding how processes are executed in an organisation. Several models have been proposed to address this…