Related papers: Interpreting Lambda Calculus in Domain-Valued Rand…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
In the theory of so called "Covariant Quantum Mechanics" a basic role is played by Hermitian vector fields on a complex line bundle in the frameworks of Galilei and Einstein spacetimes. In fact, it has been proved that the Lie algebra of…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
Deep neural networks have been well-known for their superb handling of various machine learning and artificial intelligence tasks. However, due to their over-parameterized black-box nature, it is often difficult to understand the prediction…
We are concerned with the analysis of a mean field type equation and its linearization, which is a nonlocal operator, for which we estimate the number of nodal domains for the radial eigenfunctions and the related uniqueness properties.
We define a model of predicate logic in which every term and predicate, open or closed, has an absolute denotation independently of a valuation of the variables. For each variable a, the domain of the model contains an element [[a]] which…
A systematic way of defining variants of a modeling language is useful for adopting the language to domain or project specific needs. Variants can be obtained by adopting the syntax or semantics of the language. In this paper, we take a…
We apply the machinery of projection lattices and von Neumann algebras to analyze the question of how modal interpretations can (and do) circumvent von Neumann's infamous 'no-hidden-variables' theorem.
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
The choice of making an intervention depends on its potential benefit or harm in comparison to alternatives. Estimating the likely outcome of alternatives from observational data is a challenging problem as all outcomes are never observed,…
Large Language Models (LLMs) have been recently proposed for supporting domain modeling tasks mostly related to the completion of partial models by recommending additional model elements. However, there are many more modeling tasks, one of…
We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic…
In this paper, we introduce an approach for leveraging available data across multiple locales sharing the same language to 1) improve domain classification model accuracy in Spoken Language Understanding and user experience even if new…
We describe a class calculus that is expressive enough to describe and improve its own learning process. It can design and debug programs that satisfy given input/output constraints, based on its ontology of previously learned programs. It…
To propose a mathematical model of consciousness and will, we first simulated the inverted qualia with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia on the neural network. In other words,…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…