Related papers: Proof Nets and the Complexity of Processing Center…

In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…

An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…

Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…

How do artificial neural networks bind concepts to form complex semantic structures? Here, we propose a simple neural code, whereby the existence and the type of relations between entities are represented by the distance and the direction…

The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…

Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…

One of the central aspects of contextualised language models is that they should be able to distinguish the meaning of lexically ambiguous words by their contexts. In this paper we investigate the extent to which the contextualised…

Hypothesis testing is an important cognitive process that supports human reasoning. In this paper, we introduce a computational hypothesis testing approach based on memory augmented neural networks. Our approach involves a hypothesis…

Deep learning embeddings have been successfully used for many natural language processing problems. Embeddings are mostly computed for word forms although a number of recent papers have extended this to other linguistic units like morphemes…

In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…

This informal contribution presents an ongoing line of research that is pursuing a new approach to the construction of sound proofs for the formal verification and control of complex stochastic models of dynamical systems, of reactive…

The paper discusses the role of WordNet-based semantic classification in the formalization of constructions, and more specifically in the semantic annotation of schematic fillers, in the Italian Constructicon. We outline how the Italian…

Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

Whether large language models (LLMs) process language similarly to humans has been the subject of much theoretical and practical debate. We examine this question through the lens of the production-interpretation distinction found in human…

We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity:…

Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting…

While word embeddings are currently predominant for natural language processing, most of existing models learn them solely from their contexts. However, these context-based word embeddings are limited since not all words' meaning can be…

We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…

Complex reasoning over text requires understanding and chaining together free-form predicates and logical connectives. Prior work has largely tried to do this either symbolically or with black-box transformers. We present a middle ground…