Related papers: Genericity Through Stratification
Weak-head normalization is inconsistent with functional extensionality in the call-by-name $\lambda$-calculus. We explore this problem from a new angle via the conflict between extensionality and effects. Leveraging ideas from work on the…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
Concept Bottleneck Models (CBMs) ground predictions in human-understandable concepts but face fundamental limitations: the absence of a metric to pre-evaluate concept relevance, the "linearity problem" causing recent CBMs to bypass the…
Concept bottleneck models (CBMs) have emerged as critical tools in domains where interpretability is paramount. These models rely on predefined textual descriptions, referred to as concepts, to inform their decision-making process and offer…
The Region Connection Calculus (RCC) is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The…
In this paper, we study the tedious link between the properties of sensibility and approximability of models of untyped {\lambda}-calculus. Approximability is known to be a slightly, but strictly stronger property that sensibility. However,…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
During the last decade, deep neural networks (DNN) have demonstrated impressive performances solving a wide range of problems in various domains such as medicine, finance, law, etc. Despite their great performances, they have long been…
Word embedding, specially with its recent developments, promises a quantification of the similarity between terms. However, it is not clear to which extent this similarity value can be genuinely meaningful and useful for subsequent tasks.…
This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
There is growing interest in concept-based models (CBMs) that combine high-performance and interpretability by acquiring and reasoning with a vocabulary of high-level concepts. A key requirement is that the concepts be interpretable.…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
In this mostly expository article, elements of higher category theory essential to the construction of a class of four dimensional quantum geometric models are reviewed. These models improve current state sum models for Quantum Gravity,…
Terms of Church's $\lambda$-calculus can be considered equivalent along many different definitions, but context equivalence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic,…
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these…