Related papers: Interpolation in Knowledge Representation
Much of the knowledge encoded in transformer language models (LMs) may be expressed in terms of relations: relations between words and their synonyms, entities and their attributes, etc. We show that, for a subset of relations, this…
Interpolation-based techniques become popular in recent years, as they can improve the scalability of existing verification techniques due to their inherent modularity and local reasoning capabilities. Synthesizing Craig interpolants is the…
We show that the vast majority of extensions of the description logic $\mathcal{EL}$ do not enjoy the Craig interpolation nor the projective Beth definability property. This is the case, for example, for $\mathcal{EL}$ with nominals,…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
Reinforcement Learning (RL) has achieved tremendous development in recent years, but still faces significant obstacles in addressing complex real-life problems due to the issues of poor system generalization, low sample efficiency as well…
Interpretability and explainability have gained more and more attention in the field of machine learning as they are crucial when it comes to high-stakes decisions and troubleshooting. Since both provide information about predictors and…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
Interactive machine reading comprehension (iMRC) is machine comprehension tasks where knowledge sources are partially observable. An agent must interact with an environment sequentially to gather necessary knowledge in order to answer a…
We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
Retrieval-Augmented Generation (RAG) systems have shown promise in enhancing the performance of Large Language Models (LLMs). However, these systems face challenges in effectively integrating external knowledge with the LLM's internal…
Knowledge graphs (KGs) have gained prominence for their ability to learn representations for uni-relational facts. Recently, research has focused on modeling hyper-relational facts, which move beyond the restriction of uni-relational facts…
Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms…
Knowledge graph embeddings are now a widely adopted approach to knowledge representation in which entities and relationships are embedded in vector spaces. In this chapter, we introduce the reader to the concept of knowledge graph…
We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely…
We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents,…
The recent usage of technical systems in human-centric environments leads to the question, how to teach technical systems, e.g., robots, to understand, learn, and perform tasks desired by the human. Therefore, an accurate representation of…
Embracing the pursuit of intrinsically explainable reinforcement learning raises crucial questions: what distinguishes explainability from interpretability? Should explainable and interpretable agents be developed outside of domains where…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
None of the first-order modal logics between $\mathsf{K}$ and $\mathsf{S5}$ under the constant domain semantics enjoys Craig interpolation or projective Beth definability, even in the language restricted to a single individual variable. It…