Related papers: Ultrafilter Extensions for Veltman Semantics
The paper presents a solution to the long-standing question about the decidability of the two-variable fragment of the superintuitionistic predicate logic $\mathbf{QLC}$ defined by the class of linear Kripke frames, which is also the…
In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with…
We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
Recent breakthroughs in NLP research, such as the advent of Transformer models have indisputably contributed to major advancements in several tasks. However, few works research robustness and explainability issues of their evaluation…
A logic formalism is presented which increases the expressive power of the ID/LP format of GPSG by enlarging the inventory of ordering relations and extending the domain of their application to non-siblings. This allows a concise, modular…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
Mechanistic interpretability seeks to understand the neural mechanisms that enable specific behaviors in Large Language Models (LLMs) by leveraging causality-based methods. While these approaches have identified neural circuits that copy…
Workflows constitute an important language to represent knowledge about processes, but also increasingly to reason on such knowledge. On the other hand, there is a limit to which time constraints between activities can be expressed.…
We continue the research of the relation $\hspace{1mm}\widetilde{\mid}\hspace{1mm}$ on the set $\beta {\mathbb{N}}$ of ultrafilters on ${\mathbb{N}}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
Large Language Models (LLMs) are becoming increasingly popular in pervasive computing due to their versatility and strong performance. However, despite their ubiquitous use, the exact mechanisms underlying their outstanding performance…
In this work, we study the challenge of providing human-understandable descriptions for failure modes in trained image classification models. Existing works address this problem by first identifying clusters (or directions) of incorrectly…
In-context learning (ICL) enables multimodal large language models (MLLMs) to classify images from a few labelled examples. Yet, how these models use the provided context remains opaque. While Chain-of-Thought prompting is widely used,…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…
There exist two distinct types of ultrafilter extensions of binary relations, one discovered in universal algebra and modal logic, and another, in model theory and algebra of ultrafilters. We show that the extension of the latter type is…