Related papers: Value, Representation, Information and Communicati…
A large-scale knowledge graph enhances reproducibility in biomedical data discovery by providing a standardized, integrated framework that ensures consistent interpretation across diverse datasets. It improves generalizability by connecting…
This paper develops a geometric framework for modeling belief, motivation, and influence across cognitively heterogeneous agents. Each agent is represented by a personalized value space, a vector space encoding the internal dimensions…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
A classic account of the quantification of semantic information is that of Bar-Hiller and Carnap. Their account proposes an inverse relation between the informativeness of a statement and its probability. However, their approach assigns the…
Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The representations of conditional entropy and conditional mutual information are significant in explaining the unique effects among variables. While previous studies based on conditional contrastive sampling have effectively removed…
Counterfactual reasoning is a foundational topic in both philosophical and logical studies \cite{Stalnaker1968-STAATO-5, Lewis1973-LEWC-2}. A pivotal component of counterfactual analysis is the concept of similarity between possible worlds…
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for the procedures of the classical masters. Thus, Leibniz's…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and…
Today, the vast majority of the world's digital information is represented using the fundamental assumption, introduced by Claude Shannon in 1948, that ``...the semantic aspects of communication are irrelevant to the engineering problem (of…
Emerging cyber-physical systems increasingly operate under stringent communication constraints that preclude the reliable transmission of their extensive machine-type data streams. Since raw measurements often contain correlated or…
We demonstrate the utility of a new methodological tool, neural-network word embedding models, for large-scale text analysis, revealing how these models produce richer insights into cultural associations and categories than possible with…
Despite the centrality of the notion of representation in neuroscience, the field lacks a unified framework for the concepts used to characterize representation, leading to disparate use of both terminology and measures associated with it.…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using…
The subtle human values we acquire through life experiences govern our thoughts and gets reflected in our speech. It plays an integral part in capturing the essence of our individuality and making it imperative to identify such values in…
Cosine similarity, the standard metric for measuring semantic similarity in vector spaces, is mathematically grounded in the Cauchy-Schwarz inequality, which inherently limits it to capturing linear relationships--a constraint that fails to…