Related papers: Nonstandard functional interpretations and categor…
We introduce a nonstandard extension of the category of diffeological spaces, and demonstrate its application to the study of generalized functions. Just as diffeological spaces are defined as concrete sheaves on the site of Euclidean open…
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are…
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…
A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Domain-general semantic parsing is a long-standing goal in natural language processing, where the semantic parser is capable of robustly parsing sentences from domains outside of which it was trained. Current approaches largely rely on…
We show that no total functional can uniformly transform $\Pi_1$ primality into explicit $\Sigma_1$ witnesses without violating normalization in $\mathsf{HA}$. The argument proceeds through three complementary translations: a geometric…
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
With the growing pervasiveness of artificial intelligence, the ability to explain the inferences made by machine learning models has become increasingly important. Numerous techniques for model explainability have been proposed, with…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…
This study addresses the problem of identifying the meaning of unknown words or entities in a discourse with respect to the word embedding approaches used in neural language models. We proposed a method for on-the-fly construction and…
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. H\"{o}rmander). In the hyperfunction case our work can be summarized as follows. We construct a differential algebra that…
Neural network models have achieved state-of-the-art performances in a wide range of natural language processing (NLP) tasks. However, a long-standing criticism against neural network models is the lack of interpretability, which not only…
The distinction between strong negation and default negation has been useful in answer set programming. We present an alternative account of strong negation, which lets us view strong negation in terms of the functional stable model…