Related papers: Concurrent Kleene Algebra with Observations: from …
We show how computation of left Kan extensions can be reduced to computation of free models of cartesian (finite-limit) theories. We discuss how the standard and parallel chase compute weakly free models of regular theories and free models…
Beilinson Completion Algebras (BCAs) are generalizations of complete local rings, and have a rich algebraic-analytic structure. These algebras were introduced in my paper "Traces and Differential Operators over Beilinson Completion…
Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often…
In this paper, we investigate the tendency of end-to-end neural Machine Reading Comprehension (MRC) models to match shallow patterns rather than perform inference-oriented reasoning on RC benchmarks. We aim to test the ability of these…
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address…
Artificial intelligence (AI) is increasingly used for the inverse design of materials, such as crystals and molecules. Existing AI research on molecules has integrated chemical structures of molecules with textual knowledge to adapt to…
In this paper, we show that the equational theory of relational Kleene algebra with the \emph{graph loop} operator (a.k.a.~\emph{fixset}) is \textsc{PSpace}-complete. Here, the graph loop is the unary operator that restricts a binary…
The theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
We propose in this thesis a new deformation process of Kac-Moody algebras and their representations. The direction of deformation is given by a collection of numbers, called a colouring. The natural numbers lead for example to the classical…
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…
Interpreting the internal behavior of large language models trained on code remains a critical challenge, particularly for applications demanding trust, transparency, and semantic robustness. We propose Code Concept Analysis (CoCoA): a…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a…
Recent developments in regularized Canonical Correlation Analysis (CCA) promise powerful methods for high-dimensional, multiview data analysis. However, justifying the structural assumptions behind many popular approaches remains a…
For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordinals where these relations become equal. We show that the…
Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…