Related papers: Faithful Logic Embeddings in HOL -- Deep and Shall…
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…
We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and…
The rapid rise of deepfake technology poses a severe threat to social and political stability by enabling hyper-realistic synthetic media capable of manipulating public perception. However, existing detection methods struggle with two core…
As machine learning becomes more widespread and is used in more critical applications, it's important to provide explanations for these models, to prevent unintended behavior. Unfortunately, many current interpretability methods struggle…
We find a translation with particularly nice properties from intuitionistic propositional logic in countably many variables to intuitionistic propositional logic in two variables. In addition, the existence of a possibly-not-as-nice…
Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Deep learning techniques are increasingly popular in the textual entailment task, overcoming the fragility of traditional discrete models with hard alignments and logics. In particular, the recently proposed attention models (Rockt\"aschel…
Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
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…
In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data. Background:…
Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and…
Differential dynamic logic (dL) is a formal framework for specifying and reasoning about hybrid systems, i.e., dynamical systems that exhibit both continuous and discrete behaviors. These kinds of systems arise in many safety- and…
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…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks. Reasoning with LLMs is central to solving multi-step problems and complex decision-making. To support efficient reasoning, recent studies…