Related papers: Riesz Logic
Humans can learn languages from remarkably little experience. Developing computational models that explain this ability has been a major challenge in cognitive science. Bayesian models that build in strong inductive biases - factors that…
In medicine one frequently deals with vague information. As a tool for reasoning in this area, fuzzy logic suggests itself. In this paper we explore the applicability of the basic ideas of fuzzy set theory in the context of medical…
The main objective of this paper is to develop a new semantic Network structure, based on the fuzzy sets theory, used in Artificial Intelligent system in order to provide effective on-line assistance to users of new technological systems.…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory, and lexical information for many tasks related to human-generated data. Human language makes use of a large and…
Logical rules are a popular knowledge representation language in many domains, representing background knowledge and encoding information that can be derived from given facts in a compact form. However, rule formulation is a complex process…
Many causal and policy effects of interest are defined by linear functionals of high-dimensional or non-parametric regression functions. $\sqrt{n}$-consistent and asymptotically normal estimation of the object of interest requires debiasing…
There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models and fuzzy interpretations in description logics. Fuzzy bisimulations between…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
Despite recent monumental advances in the field, many Natural Language Processing (NLP) models still struggle to perform adequately on noisy domains. We propose a novel probabilistic embedding-level method to improve the robustness of NLP…
We introduce the logical grammar emdebbing (LGE), a model inspired by pregroup grammars and categorial grammars to enable unsupervised inference of lexical categories and syntactic rules from a corpus of text. LGE produces comprehensible…
We generalize the "facial weak order" of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its…
In the present paper we show that distributional information is particularly important when considering concept availability under implicit language learning conditions. Based on results from different behavioural experiments we argue that…
Neural language models are a powerful tool to embed words into semantic vector spaces. However, learning such models generally relies on the availability of abundant and diverse training examples. In highly specialised domains this…
Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained…
The set of finite words over a well-quasi-ordered set is itself well-quasi-ordered. This seminal result by Higman is a cornerstone of the theory of well-quasi-orderings and has found numerous applications in computer science. However, this…
We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…