Related papers: Mathematics and Logic as Information Compression b…
Logic reasoning is a significant ability of human intelligence and also an important task in artificial intelligence. The existing logic reasoning methods, quite often, need to design some reasoning patterns beforehand. This has led to an…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible…
Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…
Finding desired information from large data set is a difficult problem. Information retrieval is concerned with the structure, analysis, organization, storage, searching, and retrieval of information. Index is the main constituent of an IR…
To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
In-memory computing (IMC) with single instruction multiple data (SIMD) setup enables memory to perform operations on the stored data in parallel to achieve high throughput and energy saving. To instruct a SIMD IMC hardware to compute a…
Understanding how information is dynamically accumulated and transformed in human reasoning has long challenged cognitive psychology, philosophy, and artificial intelligence. Existing accounts, from classical logic to probabilistic models,…
In the practical deployment of machine learning (ML) models, missing data represents a recurring challenge. Missing data is often addressed when training ML models. But missing data also needs to be addressed when deciding predictions and…
We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice,…
In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…
Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that…
This paper investigates how high school students in an introductory computer science course approach computing in the Logic Programming (LP) paradigm. This qualitative study shows how novice students operate within the LP paradigm while…
Music comprises of a set of complex simultaneous events organized in time. In this paper we introduce a novel framework that we call Deep Musical Information Dynamics, which combines two parallel streams - a low rate latent representation…
Incorporating semantic information into the codecs during image compression can significantly reduce the repetitive computation of fundamental semantic analysis (such as object recognition) in client-side applications. The same practice…
Compression methods, including quantization, distillation, and pruning, improve the computational efficiency of large reasoning models (LRMs). However, existing studies either fail to sufficiently compare all three compression methods on…