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The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)|size(P))…
Provenance is an increasing concern due to the ongoing revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to…
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…
Learning from large amounts of unsupervised data and a small amount of supervision is an important open problem in computer vision. We propose a new semi-supervised learning method, Semantic Positives via Pseudo-Labels (SemPPL), that…
Semi-structured query systems for document-oriented databases have many real applications. One particular application that we are interested in is matching each financial receipt image with its corresponding place of interest (POI, e.g.,…
Sandqvist's base-extension semantics for intuitionistic propositional logic defines a support relation parametrised by atomic bases, with validity identified as support in every base. Sandqvist's completeness theorem answers the global…
Accurately quantifying uncertainty in large language models (LLMs) is crucial for their reliable deployment, especially in high-stakes applications. Current state-of-the-art methods for measuring semantic uncertainty in LLMs rely on strict…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
The growing prevalence of unauthorized model usage and misattribution has increased the need for reliable model provenance analysis. However, existing methods largely rely on heuristic fingerprint-matching rules that lack provable error…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
Data analytics often involves hypothetical reasoning: repeatedly modifying the data and observing the induced effect on the computation result of a data-centric application. Previous work has shown that fine-grained data provenance can help…
We study generalized fixed-point equations over idempotent semirings and provide an efficient algorithm for the detection whether a sequence of Kleene's iterations stabilizes after a finite number of steps. Previously known approaches…
Among interpretable machine learning methods, the class of Generalised Additive Neural Networks (GANNs) is referred to as Self-Explaining Neural Networks (SENN) because of the linear dependence on explicit functions of the inputs. In binary…
The approach to proof search dubbed "coinductive proof search" (CoIPS), and previously developed by the authors for implicational intuitionistic logic, is in this paper extended to LJP, a focused sequent-calculus presentation of polarized…
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
Tabling is a powerful resolution mechanism for logic programs that captures their least fixed point semantics more faithfully than plain Prolog. In many tabling applications, we are not interested in the set of all answers to a goal, but…
Semantic parsing, i.e., the automatic derivation of meaning representation such as an instantiated predicate-argument structure for a sentence, plays a critical role in deep processing of natural language. Unlike all other top systems of…
We propose a novel approach for answering and explaining multiple-choice science questions by reasoning on grounding and abstract inference chains. This paper frames question answering as an abductive reasoning problem, constructing…
We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism,…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…