Coalgebraic Representation Theory of Fractals ( Extended

Coalgebraic Representation Theory of Fractals

The Post‐Modern Transcendental of Language in Science and Philosophy

In this chapter I discuss the deep mutations occurring today in our society and in our culture, the natural and mathematical sciences included, from the standpoint of the “transcendental of language”, and of the primacy of language over knowledge. That is, from the standpoint of the “completion of the linguistic turn” in the foundations of logic and mathematics using Peirce’s algebra of relatio...

Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone’s representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive latt...

Coalgebraic Speci cations and Models of deterministic Hybrid Systems

Coalgebraic speciication and semantics, as used earlier for object-oriented programming, is extended with temporal aspects. The (non-temporal) expression s:meth expressing that method meth is applied in state s is extended to an expression s:meth@, where is a time parameter. It means: in state s let the state evolve for units of time, and then apply method meth. With this formalism we specify v...

From Operational Chu Duality to Coalgebraic Quantum Symmetry

We pursue the principles of duality and symmetry building upon Pratt’s idea of the Stone Gamut and Abramsky’s representations of quantum systems. In the first part of the paper, we first observe that the Chu space representation of quantum systems leads us to an operational form of state-observable duality, and then show via the Chu space formalism enriched with a generic concept of closure con...