Related papers: Numbers Extensions
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed…
An attempt of a new kind of complexity anthropology is considered.
Multi-hop Question Answering (QA) is a challenging task since it requires an accurate aggregation of information from multiple context paragraphs and a thorough understanding of the underlying reasoning chains. Recent work in multi-hop QA…
Mathematical reasoning is one of the crucial abilities of general artificial intelligence, which requires machines to master mathematical logic and knowledge from solving problems. However, existing approaches are not transparent (thus not…
The notion of nondeterminism has disappeared from the current definition of NP, which has led to ambiguities in understanding NP, and caused fundamental difficulties in studying the relation P versus NP. In this paper, we question the…
The set splittability problem is the following: given a finite collection of finite sets, does there exits a single set that contains exactly half the elements from each set in the collection? (If a set has odd size, we allow the floor or…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Previous work has showcased the intriguing capability of large language models (LLMs) in retrieving facts and processing context knowledge. However, only limited research exists on the layer-wise capability of LLMs to encode knowledge,…
Large Language Models have been shown to contain extensive world knowledge in their parameters, enabling impressive performance on many knowledge intensive tasks. However, when deployed in novel settings, LLMs often encounter situations…
Declarative knowledge and procedural knowledge are two key parts in meta-cognitive theory, and these two hold significant importance in pre-training and inference of LLMs. However, a comprehensive analysis comparing these two types of…
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…
Knowledge compilation (KC) languages find a growing number of practical uses, including in Constraint Programming (CP) and in Machine Learning (ML). In most applications, one natural question is how to explain the decisions made by models…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
We study connections between definability in generalized descriptive set theory and large cardinals, under ZFC. We show that if $\kappa$ is a limit of measurables then there is no wellorder of a subset of $P(\kappa)$ of length…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…
We first show that there are practical situations in for instance forensic and gambling settings, in which applying classical probability theory, that is, based on the axioms of Kolmogorov, is problematic. We then introduce and discuss…