Related papers: NM-DEKL$^3_\infty$: A Three-Layer Non-Monotone Evo…
DEKL 2.0 is a dependent type-theoretic framework for trace-indexed knowledge evolution. Its central claim is that the proof calculus remains monotone under standard structural rules, while non-monotonic behavior arises semantically from…
Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…
We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely…
This paper introduces KOS-TL (Knowledge Operation System Type Logic), a novel constructive framework designed to provide a rigorous logical foundation for autonomous and executable knowledge systems. Traditional knowledge representation…
Recent advances in large language models (LLMs) have revolutionized the landscape of reasoning tasks. To enhance the capabilities of LLMs to emulate human reasoning, prior studies have focused on modeling reasoning steps using various…
We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To…
We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…
We define a infinitary labelled sequent calculus for PDL, G3PDL^{\infty}. A finitarily representable cyclic system, G3PDL^{\omega}, is then given. We show that both are sound and complete with respect to standard models of PDL and, further,…
Omnimodal understanding entails a massive, highly redundant search space of cross-modal interactions, demanding focused and deliberative reasoning. Current reasoning paradigms rely on either sequential step-by-step generation or parallel…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
We present M$^3$-VQA, a novel knowledge-based Visual Question Answering (VQA) benchmark, to enhance the evaluation of multimodal large language models (MLLMs) in fine-grained multimodal entity understanding and complex multi-hop reasoning.…
In discrete choice modeling (DCM), model misspecifications may lead to limited predictability and biased parameter estimates. In this paper, we propose a new approach for estimating choice models in which we divide the systematic part of…
Type-level programming is an increasingly popular way to obtain additional type safety. Unfortunately, it remains a second-class citizen in the majority of industrially-used programming languages. We propose a new dependently-typed system…
In this paper we provide an alternative semantics for Equilibrium Logic and its monotonic basis, the logic of Here-and-There (also known as G\"odel's G3 logic) that relies on the idea of "denotation" of a formula, that is, a function that…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
Large Language Models (LLMs), despite their success in question answering, exhibit limitations in complex multi-hop question answering (MQA) tasks that necessitate non-linear, structured reasoning. This limitation stems from their inability…
Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…
This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated…
Large language models (LLMs) have demonstrated remarkable capabilities across various NLP tasks. However, their computational costs are prohibitively high. To address this issue, previous research has attempted to distill the knowledge of…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…