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Independence-friendly logic is a conservative extension of first-order logic that has the same expressive power as existential second-order logic. In her Ph.D. thesis, Dechesne introduces a variant of independence-friendly logic called IFG…
For $K$ an abstract elementary class with amalgamation and no maximal models, we show that categoricity in a high-enough cardinal implies structural properties such as the uniqueness of limit models and the existence of good frames. This…
An open problem posed by Milner asks for a proof that a certain axiomatisation, which Milner showed is sound with respect to bisimilarity for regular expressions, is also complete. One of the main difficulties of the problem is the lack of…
We present a quantitative evaluation to understand the effect of zero-shot large-language model (LLMs) and prompting uses on chart reading tasks. We asked LLMs to answer 107 visualization questions to compare inference accuracies between…
We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group $G$ is strongly-graded-equivalent to the skew group algebra by a product partial action of $G$. As to a…
For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such…
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research…
Let $X$ be a set of cardinality $\kappa$ such that $\kappa^\omega=\kappa$. We prove that the linear algebra $\mathbb{R}^X$ (or $\mathbb{C}^X$) contains a free linear algebra with $2^\kappa$ generators. Using this, we prove several…
We introduce a type of zero-dimensional dynamical system (a pair consisting of a totally disconnected compact metrizable space along with a homeomorphism of that space), which we call "fiberwise essentially minimal", and we prove that the…
Zero-shot learning aims to classify visual objects without any training data via knowledge transfer between seen and unseen classes. This is typically achieved by exploring a semantic embedding space where the seen and unseen classes can be…
Computerized Adaptive Testing (CAT) is emerging as a promising testing application in many scenarios, such as education, game and recruitment, which targets at diagnosing the knowledge mastery levels of examinees on required concepts. It…
We introduce a concept, $d$-complete, and show that a Lie algebra is $d$-complete if and only if its full graph is complete.
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
We present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
This study investigates the application of large language models (LLMs), specifically GPT-3.5 and GPT-4, with Chain-of-Though (CoT) in the automatic scoring of student-written responses to science assessments. We focused on overcoming the…
This paper shows how the use of Structural Operational Semantics (SOS) in the style popularized by the process-algebra community can lead to a more succinct and useful construction for building finite automata from regular expressions. Such…
Requirements Engineering (RE) is essential for developing complex and regulated software projects. Given the challenges in transforming stakeholder inputs into consistent software designs, Qualitative Data Analysis (QDA) provides a…
We provided (PNSE'2014) expressions for free choice nets having "distributed choice property" which makes the nets "direct product" representable. In a recent work (PNSE'2016), we gave equivalent syntax for a larger class of free choice…
As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this paper, we analyze sessions with ChatGPT around topics in basic Linear Algebra. We reflect the…