Related papers: Inner models from extended logics and the Delta-op…
In this article, a model-theoretic approach is proposed to prove that the first-order G\"odel logic, $\mathbf{G}$, as well as its extension $\mathbf{G}^\Delta$ associated with first-order relational languages enjoy the Craig interpolation…
We prove that $\delta$-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications…
Scaling up multimodal models has enabled remarkable advances in visual understanding and reasoning, but practical demands call for smaller, efficient systems. In this work, we conduct a principled analysis of downscaling intelligence in…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
Reasoning is an integral part of many tasks performed by language models (LMs). However, the effects of scaling model sizes and data on reasoning abilities at pretraining time remain understudied. To rigorously investigate this problem, we…
Large language models (LLMs) have demonstrated impressive capabilities, yet their internal mechanisms for handling reasoning-intensive tasks remain underexplored. To advance the understanding of model-internal processing mechanisms, we…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
The satisfiability problem of the branching time logic CTL is studied in terms of computational complexity. Tight upper and lower bounds are provided for each temporal operator fragment. In parallel, the minimal model size is studied with a…
How human cognitive abilities are formed has long captivated researchers. However, a significant challenge lies in developing meaningful methods to measure these complex processes. With the advent of large language models (LLMs), which now…
The use of a necessity modality in a typed $\lambda$-calculus can be used to separate it into two regions. These can be thought of as intensional vs. extensional data: data in the first region, the modal one, are available as code, and…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
In-Context Learning (ICL) enables transformer-based language models to adapt to new tasks by conditioning on demonstration examples. However, traditional example-driven in-context learning lacks explicit modules for knowledge retrieval and…
Large language models (LLMs) exhibit compelling linguistic behaviour, and sometimes offer self-reports, that is to say statements about their own nature, inner workings, or behaviour. In humans, such reports are often attributed to a…
We investigate higher-dimensional $\Delta$-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical $\Delta$-system lemma. We focus in particular on…
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
The ability to interpret Machine Learning (ML) models is becoming increasingly essential. However, despite significant progress in the field, there remains a lack of rigorous characterization regarding the innate interpretability of…
Large language models (LLMs) exhibit emergent behaviors suggestive of human-like reasoning. While recent work has identified structured conceptual representations within these models, it remains unclear whether they functionally rely on…
We investigate the large order aspects of the delta-expansion under the estimation procession of the critical quantities. As illustrative examples, we revisit one-dimensional Ising model for the analytic study and two-dimensional square…
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…