Related papers: The Relational Machine Calculus
Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various…
We introduce $\mathsf{LEM}$, a type-assignment system for the linear $ \lambda $-calculus that extends second-order $\mathsf{IMLL}_2$, i.e., intuitionistic multiplicative Linear Logic, by means of logical rules that weaken and contract…
We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…
Human brain possesses the ability to effectively focus on important environmental components, which enhances perception, learning, reasoning, and decision-making. Inspired by this cognitive mechanism, we introduced a novel concept termed…
Existing formalisms for the algebraic specification and representation of networks of reversible agents suffer some shortcomings. Despite multiple attempts, reversible declensions of the Calculus of Communicating Systems (CCS) do not offer…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…
Dataflow matrix machines are self-referential generalized recurrent neural nets. The self-referential mechanism is provided via a stream of matrices defining the connectivity and weights of the network in question. A natural question is:…
Nondeterminism introduced by race conditions and message reorderings makes parallel and distributed programming hard. Nevertheless, promising approaches such as LVars and CRDTs address this problem by introducing a partial order structure…
Without any doubt, the relational paradigm has been a huge success. At the same time, we believe that the time is ripe to rethink how database systems could look like if we designed them from scratch. Would we really end up with the same…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
A Learning Model Predictive Controller (LMPC) for linear system in presented. The proposed controller is an extension of the LMPC [1] and it aims to decrease the computational burden. The control scheme is reference-free and is able to…
Interactive behaviors are ubiquitous in modern cryptography, but are also present in $\lambda$-calculi, in the form of higher-order constructions. Traditionally, however, typed $\lambda$-calculi simply do not fit well into cryptography,…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
This paper proposes a new neural architecture for collaborative ranking with implicit feedback. Our model, LRML (\textit{Latent Relational Metric Learning}) is a novel metric learning approach for recommendation. More specifically, instead…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that…
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…