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Autonomous agents are supposed to be able to finish tasks or achieve goals that are assigned by their users through performing a sequence of actions. Since there might exist multiple plans that an agent can follow and each plan might…
Reasoning is a fundamental cognitive process underlying inference, problem-solving, and decision-making. While large language models (LLMs) demonstrate strong reasoning capabilities in closed-world settings, they struggle in open-ended and…
Recent progress in large language models (LLMs) has demonstrated the ability to learn and leverage Internet-scale knowledge through pre-training with autoregressive models. Unfortunately, applying such models to settings with embodied…
The focus of this paper is to propose a driver model that incorporates human reasoning levels as actions during interactions with other drivers. Different from earlier work using game theoretical human reasoning levels, we propose a dynamic…
Grounding the common-sense reasoning of Large Language Models (LLMs) in physical domains remains a pivotal yet unsolved problem for embodied AI. Whereas prior works have focused on leveraging LLMs directly for planning in symbolic spaces,…
In this paper, we give some necessary and sufficient conditions for weighted conditional expectation type operators on L2 to be centered. Also, we investigate the relation between normal and centered weighted con- ditional type operators.…
We consider a temporal logic EF+F^-1 for unranked, unordered finite trees. The logic has two operators: EF\phi, which says "in some proper descendant \phi holds", and F^-1\phi, which says "in some proper ancestor \phi holds". We present an…
We prove the invertibility of the relevant single and double layer potentials associated to some generalizations of the Stokes operator on bounded domains. In order to do that, we first develop an ``algebra tool kit'' to deal with limit and…
Analogy is a central faculty of human intelligence, enabling abstract patterns discovered in one domain to be applied to another. Despite its central role in cognition, the mechanisms by which Transformers acquire and implement analogical…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
This paper explores the notions of $\mathcal{F}$-transitivity and topological $\mathcal{F}$-recurrence for backward shift operators on weighted $\ell^p$-spaces and $c_0$-spaces on directed trees, where $\mathcal{F}$ represents a Furstenberg…
The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…
We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
In this paper, we claim that 3D visual grounding is the cornerstone of spatial reasoning and introduce the Grounded-Spatial Reasoner (GS-Reasoner) to explore the effective spatial representations that bridge the gap between them. Existing…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…
Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between…