Niels Voorneveld

Niels Voorneveld, Peeter Laud

We propose a method for reasoning about trust in multi-agent systems, specifying a language for describing communication protocols and making trust assumptions and derivations. This is given an interpretation in a modal logic for describing the beliefs and communications of agents in a network. We define how information in the network can be shared via forwarding, and how trust between agents can be generalized to trust across networks. We give specifications for the modal logic which can be readily adapted into a lambda calculus of proofs. We show that by nesting modalities, we can describe chains of communication between agents, and establish suitable notions of trust for such chains. We see how this can be applied to trust models in public key infrastructures, as well as other interaction protocols in distributed systems.

Chad Nester, Niels Voorneveld

We present a term rewriting system that models the dynamic aspects of the free cornering with protocol choice of a monoidal category, which has been proposed as a categorical model of process interaction. This term rewriting system is confluent and terminating in an appropriate sense. We use this machinery to prove a coherence theorem for the free cornering with protocol choice.

Chad Nester, Niels Voorneveld

We present a calculus that models a simple sort of process interaction. Our calculus consists of a collection of terms together with a rewrite relation, parameterised by an arbitrary multicategory whose morphisms we understand as non-interactive processes. We show that our calculus is confluent and terminating, and that terms modulo the induced convertibility relation form a virtual double category. We relate our calculus to the free cornering of a monoidal category, which is a double-categorical model of process interaction that is similar in spirit to the calculus presented herein. Precisely, we construct a functor from the virtual double category given by our calculus into the underlying virtual double category of the free cornering of the free monoidal category on the multicategory of non-interacting processes. If we think of the terms of our calculus as programs and the rewriting system as an operational semantics for these programs, this functor gives a sound denotational semantics for our calculus in terms of the free cornering.