Related papers: Composing Codensity Bisimulations
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
We consider learning and compositionality as the key mechanisms towards simulating human-like intelligence. While each mechanism is successfully achieved by neural networks and symbolic AIs, respectively, it is the combination of the two…
Establishing equivalences between programs or systems is crucial both for verifying correctness of programs, by establishing that two implementations are equivalent, and for justifying optimisations and program transformations, by…
Compositionality has traditionally been understood as a major factor in productivity of language and, more broadly, human cognition. Yet, recently, some research started to question its status, showing that artificial neural networks are…
In contrast to the existing approaches to bisimulation for fuzzy systems, we introduce a behavioral distance to measure the behavioral similarity of states in a nondeterministic fuzzy-transition system. This behavioral distance is defined…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet…
We present a coalgebraic framework for studying generalisations of dynamic modal logics such as PDL and game logic in which both the propositions and the semantic structures can take values in an algebra $\mathbf{A}$ of truth-degrees. More…
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
Liftings of endofunctors on sets to endofunctors on relations are commonly used to capture bisimulation of coalgebras. Lax versions have been used in those cases where strict lifting fails to capture bisimilarity, as well as in modeling…
It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of…
Modern distributed systems often rely on so called weakly-consistent databases, which achieve scalability by sacrificing the consistency guarantee of distributed transaction processing. Such databases have been formalised in two different…
Predictive processing and active inference posit that the brain is a system performing Bayesian inference on the environment. By virtue of this, a prominent interpretation of predictive processing states that the generative model (a POMDP)…
Weighted automata are a generalization of nondeterministic automata that associate a weight drawn from a semiring $K$ with every transition and every state. Their behaviours can be formalized either as weighted language equivalence or…
Cellular automata provide models of parallel computation based on cells, whose connectivity is given by an action of a monoid on the cells. At each step in the computation, every cell is decorated with a state that evolves in discrete steps…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
In this paper we show how the abstract behaviours of higher-order systems can be modelled as final coalgebras of suitable behavioural functors. These functors have the challenging peculiarity to be circularly defined with their own final…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
Data collection has become an increasingly important problem in robotic manipulation, yet there still lacks much understanding of how to effectively collect data to facilitate broad generalization. Recent works on large-scale robotic data…