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Large reasoning models have demonstrated remarkable performance on complex reasoning tasks, yet the excessive length of their chain-of-thought outputs remains a major practical bottleneck due to high computation cost and poor deployability.…
We modify a canonical experimental design to identify the effectiveness of retractions. Comparing beliefs after retractions to beliefs (a) without the retracted information and (b) after equivalent new information, we find that retractions…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
A very desirable Datalog extension investigated by many researchers in the last thirty years consists in allowing the use of the basic SQL aggregates min, max, count and sum in recursive rules. In this paper, we propose a simple…
A main property of support vector machines consists in the fact that only a small portion of the training data is significant to determine the maximum margin separating hyperplane in the feature space, the so called support vectors. In a…
Data analytics often involves hypothetical reasoning: repeatedly modifying the data and observing the induced effect on the computation result of a data-centric application. Recent work has proposed to leverage ideas from data provenance…
A systematic algebraic framework for composing and decomposing logic programs is currently missing, limiting our ability to analyze and construct programs in a modular way. In this paper, we introduce set-like operations for (propositional…
Belief integration methods are often aimed at deriving a single and consistent knowledge base that retains as much as possible of the knowledge bases to integrate. The rationale behind this approach is the minimal change principle: the…
Extensive work has shown that the performance and interpretability of commonsense reasoning can be improved via knowledge-augmented reasoning methods, where the knowledge that underpins the reasoning process is explicitly verbalized and…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…
This paper proposes a new theoretical perspective for studying the Hodge conjecture through an analytical framework based on constraint geometry. Our theory begins with a key observation: in compatible pair Spencer theory, a "differential…
We propose an information-fusion approach based on belief functions to combine convolutional neural networks. In this approach, several pre-trained DS-based CNN architectures extract features from input images and convert them into mass…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Recent years have witnessed an increasing interest in training machines with reasoning ability, which deeply relies on accurately and clearly presented clue forms. The clues are usually modeled as entity-aware knowledge in existing studies.…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
Intentions are crucial for our practical reasoning. The rational intention obeys some simple logical principles, such as agglomeration and consistency, among others, motivating the search for a proper logic of intention. However, such a…
Knowledge Measures (KMs) aim at quantifying the amount of knowledge/information that a knowledge base carries. On the other hand, Belief Change (BC) is the process of changing beliefs (in our case, in terms of contraction, expansion and…