Related papers: Grounding Operators: Transitivity and Trees, Logic…
We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential…
Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between…
Behavior Trees (BTs) offer a powerful paradigm for designing modular and reactive robot controllers. BT planning, an emerging field, provides theoretical guarantees for the automated generation of reliable BTs. However, BT planning…
A robot's ability to understand or ground natural language instructions is fundamentally tied to its knowledge about the surrounding world. We present an approach to grounding natural language utterances in the context of factual…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
Models designed for intelligent process automation are required to be capable of grounding user interface elements. This task of interface element grounding is centred on linking instructions in natural language to their target referents.…
We study surface and line operators in the GL-twisted N=4 gauge theory in four dimensions. Their properties depend on the parameter t which determines the BRST operator of theory. For t=i we propose a complete description of the 2-category…
It is shown how to define difference operators and equations on particular lattices $\{x_n\}$, $2n\in\mathbb{Z}$, such that the divided difference operator $(\mathcal{D}f)(x_{n+1/2})= (f(x_{n+1})-f(x_n))/(x_{n+1}-x_n)$ has the property that…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
When an agent can articulate why something works, we typically take this as evidence of genuine understanding. This presupposes that effective action and correct explanation covary, and that coherent explanation reliably signals both. I…
In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators…
How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
This paper examines bilateral claims problems with lower and upper exclusion thresholds that determine whether an individual is excluded from initial gains or losses. We introduce the exclusion dilation operator, a method that transforms…
AI agents -- systems that combine foundation models with reasoning, planning, memory, and tool use -- are rapidly becoming a practical interface between natural-language intent and real-world computation. This survey synthesizes the…
We count invertible Schr\"odinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fieldsfor trees, cycles and complete graphs.This is achieved for trees through the definition and use of local invariants…
The striking recent advances in eliciting seemingly meaningful language behaviour from language-only machine learning models have only made more apparent, through the surfacing of clear limitations, the need to go beyond the language-only…
The lifted dynamic junction tree algorithm (LDJT) efficiently answers filtering and prediction queries for probabilistic relational temporal models by building and then reusing a first-order cluster representation of a knowledge base for…
We investigate the expressivity and computational complexity of two modal logics on finite forests equipped with operators to reason on submodels. The logic ML(|) extends the basic modal logic ML with the composition operator | from static…
Compositional generalization remains a foundational weakness of modern neural networks, limiting their robustness and applicability in domains requiring out-of-distribution reasoning. A central, yet unverified, assumption in neuro-symbolic…