Resource Semantics

A system of logic with:

• An interpretation of its formulae as assertions about states of processes expressed in terms of the manipuated processes.

Categorical Semantics

$$\begin{array}{rl}\text{Ordered monoid }& (R,\circ ,e,⊑)\\ r\models p& ⟺r\in \mathcal{V}(p)\\ r\models \varphi \to \psi & ⟺\forall s⊑r.s\models \varphi ⟹s\models \psi \\ r\models I& ⟺r⊑e\\ r\models \varphi \ast \psi & ⟺\exists s,t:World.r⊑(s\circ t)\wedge s\models \varphi \wedge t\models \psi \end{array}$$

$\ast$ - resource sharing $-\ast$

Notes

Distributed System Metaphor Multiplicative Linear Logic Bunched Implication Source: http://www0.cs.ucl.ac.uk/staff/D.Pym/MGS_2025_4.pdf