Standpoint logics offer unified modal logic-based formalisms for representing multiple heterogeneous viewpoints. At the same time, many non-monotonic reasoning frameworks can be naturally captured using modal logics - in particular using the modal logic S4F. In this work, we propose a novel formalism called S4F Standpoint Logic, which generalises both S4F and propositional standpoint logic and is therefore capable of expressing multi-viewpoint, non-monotonic semantic commitments. We define its syntax and semantics and analyze its computational complexity, obtaining the result that S4F Standpoint Logic is not computationally harder than its constituent logics, whether in monotonic or non-monotonic form. We also outline mechanisms for credulous and sceptical acceptance and illustrate the framework with an example.

The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient reasoning and computational techniques for such a combined formalism presents a significant challenge. In this paper, we adopt a more straightforward approach aiming at integrating two well-established and computationally well-behaved components: higher-order patterns on one side and fuzzy equivalences expressed through similarity relations based on minimum T-norm on the other. We propose a unification algorithm for higher-order patterns modulo these similarity relations and prove its termination, soundness, and completeness. This unification problem, like its crisp counterpart, is unitary. The algorithm computes a most general unifier with the highest degree of approximation when the given terms are unifiable.

Current LLM pipelines account for only one possible tokenization for a given string, ignoring exponentially many alternative tokenizations during training and inference. For example, the standard Llama3 tokenization of penguin is [p,enguin], yet [peng,uin] is another perfectly valid alternative. In this paper, we show that despite LLMs being trained solely on one tokenization, they still retain semantic understanding of other tokenizations, raising questions about their implications in LLM safety. Put succinctly, we answer the following question: can we adversarially tokenize an obviously malicious string to evade safety and alignment restrictions? We show that not only is adversarial tokenization an effective yet previously neglected axis of attack, but it is also competitive against existing state-of-the-art adversarial approaches without changing the text of the harmful request. We empirically validate this exploit across three state-of-the-art LLMs and adversarial datasets, revealing a previously unknown vulnerability in subword models.

Granger causality has become an indispensable tool for analyzing causal relationships between time series. In this paper, we provide a detailed overview of its mathematical foundations, trace its historical development, and explore how recent computational advancements can enhance its application in various fields. We will not hesitate to present the proofs in full if they are simple and transparent. For more complex theorems on which we rely, we will provide supporting citations. We also discuss potential future directions for the method, particularly in the context of largescale data analysis.