Related papers: Uniform Interpolation in Distributed Knowledge Mod…
We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest…
Top-performing machine learning systems, such as deep neural networks, large ensembles and complex probabilistic graphical models, can be expensive to store, slow to evaluate and hard to integrate into larger systems. Ideally, we would like…
Craig's interpolation theorem (Craig 1957) is an important theorem known for propositional logic and first-order logic. It says that if a logical formula $\beta$ logically follows from a formula $\alpha$, then there is a formula $\gamma$,…
Knowledge-based visual question answering requires external knowledge beyond visible content to answer the question correctly. One limitation of existing methods is that they focus more on modeling the inter-modal and intra-modal…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…
After recalling the definitions of atomic and molecular logics, we show how notions of bisimulation can be automatically defined from the truth conditions of the connectives of any of these logics. Then, we prove a generalization of van…
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal…
This paper is a mathematical investigation on Epstein semantics. One of the main tools of the present paper is the model-theoretic S-set construction introduced in (Krawczyk 2022). We use it to prove several results: 1) that each Epstein…
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Structured neuron encapsulation introduces a modular framework that enables more effective aggregation and specialization of information within deep learning architectures. A model modified through this framework demonstrated improved…
In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…
We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…
Deep learning has emerged as a versatile tool for a wide range of NLP tasks, due to its superior capacity in representation learning. But its applicability is limited by the reliance on annotated examples, which are difficult to produce at…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to…
Knowledge distillation has emerged as an effective strategy for compressing large language models' (LLMs) knowledge into smaller, more efficient student models. However, standard one-shot distillation methods often produce suboptimal…
The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
Distributed knowledge is the sum of the knowledge in a group; what someone who is able to discern between two possible worlds whenever any member of the group can discern between them, would know. Sometimes distributed knowledge is referred…