Related papers: The parallel versus branching recurrences in compu…
There has been intensive research regarding machine learning models for predicting bankruptcy in recent years. However, the lack of interpretability limits their growth and practical implementation. This study proposes a data-driven…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In…
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…
With the advent of multi-core processors and their fast expansion, it is quite clear that {\em parallel computing} is now a genuine requirement in Computer Science and Engineering (and related) curriculum. In addition to the pervasiveness…
Concurrency and probability are both much studied extensions of sequential computation. Within concurrency theory, there is a broad divide between interleaving models and logics, which model concurrency by non-determinism, and `truly…
It is widely accepted that every system should be robust in that ``small'' violations of environment assumptions should lead to ``small'' violations of system guarantees, but it is less clear how to make this intuition mathematically…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
This paper proposes a technique to specify and verify whether a loop can be parallelised. Our approach can be used as an additional step in a parallelising compiler to verify user annotations about loop dependences. Essentially, our…
Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic…
Continual Learning (CL) is a field dedicated to devise algorithms able to achieve lifelong learning. Overcoming the knowledge disruption of previously acquired concepts, a drawback affecting deep learning models and that goes by the name of…
Continual learning (CL) provides a framework for training models in ever-evolving environments. Although re-occurrence of previously seen objects or tasks is common in real-world problems, the concept of repetition in the data stream is not…
The growing complexity of real-world systems necessitates interdisciplinary solutions to confront myriad challenges in modeling, analysis, management, and control. To meet these demands, the parallel systems method rooted in Artificial…
Learning continuously during all model lifetime is fundamental to deploy machine learning solutions robust to drifts in the data distribution. Advances in Continual Learning (CL) with recurrent neural networks could pave the way to a large…
A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect…
Despite incredible progress, many neural architectures fail to properly generalize beyond their training distribution. As such, learning to reason in a correct and generalizable way is one of the current fundamental challenges in machine…
Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…
We prove that parallel processing with homogeneous processors is logically equivalent to fast serial processing. The reverse proposition can also be used to identify obscure opportunities for applying parallelism. To our knowledge, this…