arXiv subjects

Philip Sink

Publications and source records attributed to Philip Sink.

4 recordsLinked to original sources

arXiv2026

Simplicial Actions for Distributed Protocols

This paper captures and extends some of the core results from the tech memo "A New Semantics for Belief Revision in Simplicial Complexes". As such, we set out to explore the implementation of action models in the setting of simplicial semantics for modal logic. Such an idea is not entirely new to the literature, showing up in both "A simplicial complex model for dynamic epistemic logic to study distributed task computability" and "Knowledge and Simplicial Complexes". However, we will explore action models in a more general setting. In particular, we will allow for action models for simplicial models for belief, as in "A Semantics for Belief in Simplicial Complexes". This will let us incorporate the notion of belief revision, as developed in "Simplicial Semantics for Belief Revision", into these action models. Moreover, we explicitly connect action models in the simplicial setting to distributed protocols as defined in the textbook "Distributed Computing Through Combinatorial Topology". We conclude with some speculation on how we might interpret distributed protocols with revision.

cs.LO↗

arXiv2026

Simplicial Semantics for Belief Revision

This paper will give a definition of belief revision within simplicial semantics. Starting from the work presented in "A Semantics for Belief in Simplicial Complexes" as a baseline, this paper modifies the semantics for belief given there to allow atomic formulae to be assigned to nodes, not facets. Conceptually and philosophically, this version of the semantics is better suited if one wishes to interpret the nodes of a simplicial model of epistemic logic as a "perspective" assigned to a particular agent. If nodes are perspectives, it then follows that worlds, or the facets of a simplicial model, are composed themselves of perspectives. This allows us to say that two worlds are more similar, or "nearer", if they share more perspectives. With this conceptual notion of nearness in hand, two different formal presentations of revision are given. We conclude by exploring some conceptual pitfalls surrounding these definitions under iterated revision, and motivate a few potential solutions that involve giving the agents a "memory" of what has been announced so far.

cs.LO↗

arXiv2025

A Semantics for Belief in Simplicial Complexes

We provide novel semantics for belief using simplicial complexes. In our framework, belief is a KD45 modality that satisfies "knowledge implies belief" ("If you know phi, then you believe phi"); in addition, we adopt the (standard) assumption that each facet in our simplicial models contains exactly one vertex for each agent. No existing model of belief in simplicial complexes that we are aware of is able to satisfy all of these conditions without trivializing belief to coincide with knowledge. We establish a truth-preserving correspondence between our simplicial framework and standard relational models for knowledge and belief; this involves, notably, proving that all relational models can be simulated using proper relational models, a result of independent interest. Finally, we apply these results to provide a simple axiomatization.

cs.LO↗

arXiv2025

A Note on Proper Relational Structures

In this note we provide an algorithm for translating relational structures into "proper" relational structures, i.e., those such that there is no pair of worlds w and u such that w is accessible from u for every agent. In particular, our method of translation preserves many classical properties of relational structures, such as transitivity and the Euclidean property. As a result, this method of translation has many applications in the literature on Simplicial Semantics for modal logic, where the creation of proper canonical relational structures is a common step in proofs of completeness.

cs.LO↗