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Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose a simple
Externí odkaz:
http://arxiv.org/abs/2410.10643
We introduce effectful Mealy machines - a general notion of Mealy machine with global effects - and give them semantics in terms of both effectful bisimilarity and traces. Bisimilarity of effectful Mealy machines is characterised syntactically in ter
Externí odkaz:
http://arxiv.org/abs/2410.10627
Tape diagrams provide a convenient notation for arrows of rig categories, i.e., categories equipped with two monoidal products, $\oplus$ and $\otimes$, where $\otimes$ distributes over $\oplus $. In this work, we extend tape diagrams with traces over
Externí odkaz:
http://arxiv.org/abs/2410.03561
Autor:
Barbiero, Pietro, Fioravanti, Stefano, Giannini, Francesco, Tonda, Alberto, Lio, Pietro, Di Lavore, Elena
Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation" which still
Externí odkaz:
http://arxiv.org/abs/2304.14094
Autor:
Di Lavore, Elena, Román, Mario
We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a synthetic Bayes th
Externí odkaz:
http://arxiv.org/abs/2301.12989
Publikováno v:
Il Foro Italiano, 1975 Jul 01. 98(7/8), 1749/1750-1753/1754.
Externí odkaz:
https://www.jstor.org/stable/23164337
We introduce monoidal streams. Monoidal streams are a generalization of causal stream functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric monoidal categories. In the same way that streams provide semantics to data
Externí odkaz:
http://arxiv.org/abs/2212.14494
Autor:
Di Lavore, Elena, Sobociński, Paweł
Publikováno v:
Logical Methods in Computer Science, Volume 19, Issue 3 (September 4, 2023) lmcs:10552
We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition:
Externí odkaz:
http://arxiv.org/abs/2212.13229
Autor:
Niccolini, G.
Publikováno v:
Il Foro Italiano, 1976 Jan 01. 99, 725/726-727/728.
Externí odkaz:
https://www.jstor.org/stable/23173429
Publikováno v:
Il Foro Italiano, 1976 Jan 01. 99, 889/890-891/892.
Externí odkaz:
https://www.jstor.org/stable/23173461