Related papers: Categorical semantics of a simple differential pro…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
Without prior knowledge, distinguishing different languages may be a hard task, especially when their borders are permeable. We develop an extension of spectral clustering -- a powerful unsupervised classification toolbox -- that is shown…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
Programming by Example (PBE) is the task of inducing computer programs from input-output examples. It can be seen as a type of machine learning where the hypothesis space is the set of legal programs in some programming language. Recent…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
In machine learning (ML), researchers and engineers seem to be at odds. System implementers would prefer models to be declarative, with detailed type information and semantic restrictions that allow models to be optimised, rearranged and…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
How do the synthetic neurons in language models create "thought categories" to segment and analyze their informational environment? What are the cognitive characteristics, at the very level of formal neurons, of this artificial categorical…
In the past years, software reverse engineering dealt with source code understanding. Nowadays, it is levered to software requirements abstract level, supported by feature model notations, language independent, and simpler than the source…
Deep learning has seen tremendous success over the past decade in computer vision, machine translation, and gameplay. This success rests in crucial ways on gradient-descent optimization and the ability to learn parameters of a neural…
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.
This survey presents in some detail the main advances that have been recently taking place in Computational Linguistics towards the unification of the two prominent semantic paradigms: the compositional formal semantics view and the…
Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for…