Related papers: Interpreting Lambda Calculus in Domain-Valued Rand…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…
A domain-theoretic framework is presented for validated robustness analysis of neural networks. First, global robustness of a general class of networks is analyzed. Then, using the fact that Edalat's domain-theoretic L-derivative coincides…
The proliferation of deep neural networks in various domains has seen an increased need for interpretability of these models. Preliminary work done along this line and papers that surveyed such, are focused on high-level representation…
Through extensive experience developing and explaining machine learning (ML) applications for real-world domains, we have learned that ML models are only as interpretable as their features. Even simple, highly interpretable model types such…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
We study the evolution of biased domain walls in the early universe. We explicitly discuss the roles played by the surface tension and volume pressure in the evolution of the walls, and quantify their effects by looking at the collapse of…
We analyse a simple model with just a $\Lambda$ term present. Differing results are obtained depending on the boundary conditions applied. HH boundary conditions give the factor exp(1/Lambda) but in agreement with Rubakov et al. is badly…
Representation learning is an essential problem in a wide range of applications and it is important for performing downstream tasks successfully. In this paper, we propose a new model that learns coupled representations of domains, intents,…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
Delimited control operator shift0 exhibits versatile capabilities: it can express layered monadic effects, or equivalently, algebraic effects. Little did we know it can express lambda calculus too! We present $ \Lambda_\$ $, a call-by-value…
We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value…
A framework for consensus modelling is introduced using Kleene's three valued logic as a means to express vagueness in agents' beliefs. Explicitly borderline cases are inherent to propositions involving vague concepts where sentences of a…
We investigate how different domains are encoded in modern neural network architectures. We analyze the relationship between natural language domains, model size, and the amount of training data used. The primary analysis tool we develop is…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
Large language models (LLMs) have exhibited impressive competence in various tasks, but their internal mechanisms on mathematical problems are still under-explored. In this paper, we study a fundamental question: how language models encode…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
Neural networks are powerful tools for cognitive modeling due to their flexibility and emergent properties. However, interpreting their learned representations remains challenging due to their sub-symbolic semantics. In this work, we…
A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the…
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive…