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.

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Pages

Posts

Future Blog Post

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Blog Post number 4

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Blog Post number 3

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Blog Post number 2

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Blog Post number 1

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

portfolio

publications

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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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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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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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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Published in , 1900

talks

A Logical Model of Pluralistic Ignorance

Published:

Much of the existing literature on pluralistic ignorance suggests that agents who find themselves in such a situation must consider themselves “special” in one way or another (Grosz 2018, Bjerring et al. 2014). Agents have to recognize their own dishonesty, but believe everyone around them is perfectly honest. This argument is taken to show that pluralistic ignorance is irrational. Modifying work from Christoff 2016, we use a simple logical model to show that these arguments for the irrationality of pluralistic ignorance depend on various introspection assumptions. We will finish by putting forth various scenarios where agents can be honest, headstrong, or something similar (generally taken to be impossible under pluralistic ignorance) but are nonetheless consistent if one relaxes introspection assumptions. This shows that agents can see themselves as no different from their friends and still be in a situation of pluralistic ignorance with sufficiently weak introspection assumptions.

Modal Logic Without Possible Worlds

Published:

Joint talk with Brittany Gelb. We presented a semantics for modal logic based on simplicial complexes that instead of possible worlds uses an “Agent Perspective”. Philip explained the details of the formalism, including a novel soundness and completeness proof. Brittany followed up with some applications of these models to a distributed setting. Additionally, she showed how we can use tools from algebraic topology to show a variety of things including the nonexistence of bisimulations.

Modal Logic Without Possible Worlds

Published:

Joint talk with Brittany Gelb. We presented a semantics for modal logic based on simplicial complexes that instead of possible worlds uses an “Agent Perspective”. Philip explained the details of the formalism, including a novel soundness and completeness proof. Brittany followed up with some applications of these models to a distributed setting. Additionally, she showed how we can use tools from algebraic topology to show a variety of things including the nonexistence of bisimulations.

Philosophy Then and Now: A Re-Evaluation of Rorty’s Philosophical Pessimism

Published:

This was a talk I was invited to give at a special session of the Richard Rorty Society by Dr. David Rondel. The main goal of the talk was to compare and contrast the metaphilosphies of Richard Rorty and Philip Kitcher, with the ultimate goal of showing that each has something to inform the other. In particular, each misses something of value the other catches. Rorty is ultimately overly skeptical of both formal philosophy, and both are overly skeptical of various politically motivated philosophical projects. However, Rorty’s views on this latter topic notably evolved in complex ways over time.

Description Fitting and Alan Turing

Published:

Joint talk with Stephen Perry.

One classic question of 20th century philosophy, inspired by Wigner’s classic 1960 paper, is “Why is mathematics, something abstract, so applicable to the sciences, something empirical?” A new analytical tool, description fitting, seeks to ease our mind about such questions. There is no one, singular way that applied mathematics works. Rather, the particular goals relative to each project inform how each piece of applied mathematics “works”. Applied mathematicians will massage, or “fit” their description of the natural world, sometimes in very idealized or even false ways, in order to make that description amenable to formalization.

An Implementation of Belief Revision in Simplicial Models for Dynamic Epistemic Logic

Published:

In this talk we set out to show how to connect belief revision to dynamic epistemic logic by leveraging tools given by the setting of simplicial semantics. We start by modifying some of the existing models for DEL in simplicial semantics (“Knowledge and Simplicial Complexes”, “A Simplicial Complex Model for Dynamic Epistemic Logic”). In particular, we will show how to modify these models for DEL so that they work in a setting for belief, rather than knowledge, using tools from the upcoming paper “Belief In Simplicial Complexes”. With this in hand, we will then motivate an endogenous notion of “nearness” between facets, where two facets sharing more perspectives in common is interpreted as the two facets being more similar. We exploit this notion of “nearness” to give a model for belief revision ala Lewis’ “Probabilities of Conditionals and Conditional Probabilities”, and ultimately we use this notion of nearness to give a model of DEL where agents update via revision, rather than classically. We will conclude with a discussion of some existing and future work which attempts to exploit this notion of nearness to give new tools for fault tolerance.

teaching

TA for 80-150 ‘‘Nature of Reason’’

Undergraduate course, Carnegie Mellon University, Department of Philosophy, 2021

TA for the course 80-150 ‘‘Nature of Reason’’, with Instructor of Record Dr. Francesca Zaffora Blando. Description from here.