Related papers: Domain Reasoning in TopKAT
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, composite mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity,…
As large language models (LLMs) perform more difficult tasks, it becomes harder to verify the correctness and safety of their behavior. One approach to help with this issue is to prompt LLMs to externalize their reasoning, e.g., by having…
Reasoning with minimal models has always been at the core of many knowledge representation techniques, but we still have only a limited understanding of this problem in Description Logics (DLs). Minimization of some selected predicates,…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions.…
We investigate the scaling properties of implicit deductive reasoning over Horn clauses in depth-bounded Transformers. By systematically decorrelating provability from spurious features and enforcing algorithmic alignment, we find that in…
Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small…
Formal XAI (explainable AI) is a growing area that focuses on computing explanations with mathematical guarantees for the decisions made by ML models. Inside formal XAI, one of the most studied cases is that of explaining the choices taken…
Reliable biomedical and clinical retrieval requires more than strong ranking performance: it requires a practical way to find systematic model failures and curate the training evidence needed to correct them. Late-interaction models such as…
General program equivalence is undecidable. However, if we abstract away the semantics of statements, then this problem becomes not just decidable, but practically feasible. For instance, a program of the form "if $b$ then $e$ else $f$"…
The CAP theorem states that a distributed system cannot simultaneously guarantee consistency, availability, and partition tolerance under network partition. Inspired by this result, this paper formulates a CAP-like conjecture for Large…
Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class of domain-range semigroups with demonic composition is not finitely axiomatisable. We extend the…
Chain-of-Thought (CoT) reasoning enables Large Language Models (LLMs) to solve complex reasoning tasks by generating intermediate reasoning steps. However, most existing approaches focus on hard token decoding, which constrains reasoning…
Concept-based Models are a class of inherently explainable networks that improve upon standard Deep Neural Networks by providing a rationale behind their predictions using human-understandable `concepts'. With these models being highly…
Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming…