Related papers: Ordinal Motifs in Lattices
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
We present a statistical mechanical theory of the process of annotating an object with terms selected from an ontology. The term selection process is formulated as an ideal lattice gas model, but in a highly structured inhomogeneous field.…
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with…
Robotic systems for household object rearrangement often rely on latent preference models inferred from human demonstrations. While effective at prediction, these models offer limited insight into the interpretable factors that guide human…
The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…
Ordinal Classification (OC) is a widely encountered challenge in Natural Language Processing (NLP), with applications in various domains such as sentiment analysis, rating prediction, and more. Previous approaches to tackle OC have…
Neural rationale models are popular for interpretable predictions of NLP tasks. In these, a selector extracts segments of the input text, called rationales, and passes these segments to a classifier for prediction. Since the rationale is…
Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic…
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
Large language models (LLMs) have exhibited remarkable capabilities in learning from explanations in prompts, but there has been limited understanding of exactly how these explanations function or why they are effective. This work aims to…
This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
The purpose of this paper is to explore some semantic problems related to the use of linguistic ontologies in information systems, and to suggest some organizing principles aimed to solve such problems. The taxonomic structure of current…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…