Philip Sink

Philip Sink

he/him

Recently graduated PhD Student in Logic, Computation, and Methodology in the Philosophy Department at Carnegie Mellon University.
My main area of study is Modal Logic, with a focus on Simplicial Semantics and applications to Distributed Computing.

Publications

You can also find my articles on my Google Scholar profile.

Conference Proceedings

A Semantics for Belief in Simplicial Complexes

Published in Proceedings of AiML 2026, 2026

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.

Recommended citation: Adam Bjorndahl and Philip Sink (2026). "A Semantics for Belief in Simplicial Complexes" Proceedings of AiML 2026
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Technical Reports

A New Semantics for Belief Revision in Simplicial Complexes

Published in NASA Technical Reports Server, 2026

In this paper we set out to develop a novel method for handling transient faults in gossip protocols. In particular, we are interested in settings where a signal “P” can come across the network, followed by a signal “¬P” at a later time. These signals could even come from the same agent, and any agent is capable of failing as such. The main idea to handle such a dramatically faulty setting is to use a technique from the philosophical literature called “belief revision”. [31] This allows agents to update on information contrary to their beliefs without resorting to probabilities. However, belief revision is often difficult to implement in a practical setting. Therefore, we turn towards using simplicial semantics for epistemic modal logic to represent each single time-slice of a protocol. Such models already have a history of applications in distributed computing. [25] [36] [19] [26] [24] [22] [23] [29] In order to model the transitions between time slices, we will use action models. These too already have a history in distributed computing. [26] [19] [3] [34] [39] [15] We will modify the application of action models to simplicial complexes in order to incorporate belief revision. In so doing, we will be able to define a novel gossip protocol for handling the prescribed fault scenario.

Recommended citation: Philip Sink and Alwyn Goodloe (2026). "A New Semantics for Belief Revision in Simplicial Complexes" NASA Technical Reports Server
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Modal Logic Without Possible Worlds: A New Semantics for Modal Logic in Simplicial Complexes

Published in NASA Technical Reports Server, 2022

In this paper, we set out to give a novel semantics for modal logic in simplicial complexes. The motivation for this semantics will be first the replacement of possible worlds with the idea of an “agent perspective”. After exploring some of the philosophical implications of such a move, we give a semantics based around this idea. Following this, we explore some of the more interesting consequences of such a system, in particular the soundness of an unusual axiom we call NU^*. After giving soundness and completeness, we conclude by exploring ways to weaken this axiom in our semantics.

Recommended citation: Philip Sink (2022). "Modal Logic Without Possible Worlds: A New Semantics for Modal Logic in Simplicial Complexes" NASA Technical Reports Server
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Under Review

Description Fitting and Alan Turing

Published in N/A, 2026

This paper sets out to do two things. First, we introduce a novel approach for analyzing applied mathematics, called “Description Fitting”. This methodology attempts to understand the success of a piece of applied mathematics by analyzing the choices made by the applied mathematician in how they choose to “describe” both the informal, target phenomena and the mathematics they hope will effectively model it. In particular, a focus is given to the goals of the modeler, and how these goals influence the descriptions themselves. With this idea in hand, we turn towards the work of Alan Turing. Our focus is on his theory of computation, and in particular his work on “On Computable Numbers, with an Application to the Entscheidungsproblem” (Turing 1936) There, Turing gives a particular account of an informal human computer, cached out in terms of what Wilfried Sieg calls “boundedness” and “locality” conditions. (Sieg 2018) We observe that how Turing sets out these descriptions seems not to be governed solely by the goal of empirical adequacy. Rather, Turing deliberately tailored these descriptions in order to make the connection to his desired formalism, “arbitrary production machines”, more salient. Moreover, this tailoring is highly motivated by the goals of giving an account of a “computable number”, à la Borel, and by giving a negative answer to the Entscheidungsproblem.

Recommended citation: N/A
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Prepublications

Simplicial Actions for Distributed Protocols

Published in arXiv, 2026

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.

Recommended citation: Philip Sink (2026). "Simplicial Actions for Distributed Protocols" arXiv
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Simplicial Semantics for Belief Revision

Published in arXiv, 2026

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.

Recommended citation: Philip Sink (2026). "Simplicial Semantics for Belief Revision" arXiv
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A Note on Proper Relational Structures

Published in arXiv, 2025

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.

Recommended citation: Adam Bjorndahl and Philip Sink (2025). "A Note on Proper Relational Structures" arXiv
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