![[Berkeley Seminar] Kris Brown | Incremental homomorphism search @ToposInstitute](https://i.ytimg.com/vi/LUOOSz1f-80/maxresdefault.jpg)
Uploaded April 2025 | Updated September 2026, 2 weeks ago
Title: Incremental homomorphism search
Abstract: An incremental search problem tries to answer how the answer set to some query changes in response to a relatively small change to underlying ground truth data. This can be much more efficient than trying to compute the answer to the new data from scratch. Moreover, in many contexts we have a fixed set of possible changes that we are anticipating, so our algorithm ought to take advantage of this extra knowledge. We'll first address this in the context of relational databases, which we model as ACSets, with the set of ACSet homomorphisms Hom(Q, X) being the answer set to a query Q, which is itself an ACSet. Then we'll generalize this story to any category with appropriate structure. This is work-in-progress, which you can check out at krisb.org/forest/math-00IG.xml.
https://topos.institute/events/berkeley-seminar/
Title: Incremental homomorphism search
Abstract: An incremental search problem tries to answer how the answer set to some query changes in response to a relatively small change to underlying ground truth data. This can be much more efficient than trying to compute the answer to the new data from scratch. Moreover, in many contexts we have a fixed set of possible changes that we are anticipating, so our algorithm ought to take advantage of this extra knowledge. We'll first address this in the context of relational databases, which we model as ACSets, with the set of ACSet homomorphisms Hom(Q, X) being the answer set to a query Q, which is itself an ACSet. Then we'll generalize this story to any category with appropriate structure. This is work-in-progress, which you can check out at krisb.org/forest/math-00IG.xml.
https://topos.institute/events/berkeley-seminar/
![[Berkeley Seminar] Kris Brown | Incremental homomorphism search](https://i.ytimg.com/vi/LUOOSz1f-80/mqdefault.jpg "[Berkeley Seminar] Kris Brown | Incremental homomorphism search
Title: Incremental homomorphism search
Abstract: An incremental search problem tries to answer how the answer set to some query changes in response to a relatively small change to underlying ground truth data. This can be much more efficient than trying to compute the answer to the new data from scratch. Moreover, in many contexts we have a fixed set of possible changes that we are anticipating, so our algorithm ought to take advantage of this extra knowledge. Well first address this in the context of relational databases, which we model as ACSets, with the set of ACSet homomorphisms Hom(Q, X) being the answer set to a query Q, which is itself an ACSet. Then well generalize this story to any category with appropriate structure. This is work-in-progress, which you can check out at https://www.krisb.org/forest/math-00IG.xml.
https://topos.institute/events/berkeley-seminar/")
![[Oxford Seminar] Ray Pedersen | Everettian QM and the problem of ontological extravagance](https://i.ytimg.com/vi/L_PKQhLrWRs/mqdefault.jpg "[Oxford Seminar] Ray Pedersen | Everettian QM and the problem of ontological extravagance
Oxford Seminar, 27th of March 2025
Title: Everettian quantum mechanics and the problem of ontological extravagance
Abstract: Since it neither relies on a collapse postulate nor posits a hidden variable, Everettian quantum mechanics (EQM) is an attractive option among realist interpretations of quantum mechanics. In some sense, EQM is a simpler theory than its competitors. However, it also appears to require more structure; unlike its competitor theories, EQM has traditionally been taken to entail a multitude of worlds, as every possible outcome of every quantum process is actualized in at least one world. Since no other realist competitor theory shares this feature, the most prominent objection raised against EQM is that of ontological extravagance.
Everettians have given this objection little serious attention, at least in part because the objection from ontological extravagance has not yet been carefully articulated in the literature. To clarify this objection, I distinguish between two types of simplicity criteria: ones concerned with ontological abundance and others concerned with postulate abundance. Where ontological abundance criteria concern the number of concrete objects that some theory posits, postulate abundance norms instead concern the number and overall complexity of the set of postulates of the theory. Unfortunately, it is unclear how we ought to weigh these simplicity-related metaphysical considerations, and worse, as I argue, there is no independent motivation for either sort. I argue that we ought to instead consider the proximity between the way the theory says the world is, and the way the world appears to be. With the deadlock between Everettians and non-Everettians on what sort of simplicity criterion reigns supreme, this severely overlooked criterion offers a promising route forward in the dialectic. This alternate criterion roughly corresponds to what Emery (2023) calls the minimal divergence norm, under which we ought to prefer theories that deviate least from the manifest image, or the way the world generally appears to be. However, such a norm requires further specification; there is no image of the world that uniquely picks out the manifest image. Observations themselves depend on our theoretical commitments, which vary from agent to agent, and so there are many manifest images. To avoid this multiplicity, I argue that we ought to look to the physical sciences for a widely-accepted theory that describes the world as we experience it. Classical mechanics (CM), the predecessor theory to quantum mechanics, does exactly that; though it is certainly not a correct description of reality, it is sufficiently accurate for numerous forms of engineering, as it describes macroscopic reality well enough. I argue that we ought to treat the way that classical mechanics says the world is as the manifest image. Then, the third type of criteria, which I call classical divergence, concerns the degree to which the way some theory in question says the world is deviates from the way that CM says the world is. I defend this norm on pragmatic grounds, arguing that adhering to it offers a distinct epistemic advantage.
While EQM does not necessarily tell us that our world is vastly different from the way that CM says it is, it is generally taken to entail many more worlds than its competitor theories. With this new set of simplicity criteria in place, Everettians can better understand the available dimensions along which they may endeavor to improve their ontology. This new norm that I advocate offers hope: Everettians can seek a less extravagant ontology by strategically minimizing classical divergence.")
![[Berkeley Seminar] Valeria de Paiva | Classical and constructive logics together: Ecumenical systems](https://i.ytimg.com/vi/M1yFhKKDrpI/mqdefault.jpg "[Berkeley Seminar] Valeria de Paiva | Classical and constructive logics together: Ecumenical systems
Title Classical and constructive logics together: Ecumenical systems
Abstract Much has been said about intuitionistic and classical logical systems since Gentzens seminal work. Recently Prawitz, Dowek and others, have been discussing how to put together Gentzens systems for classical and intuitionistic logic into a single system. This has been called Ecumenical Logic. I will present an ecumenical sequent calculus and state some of its proof theoretical properties. This approach to an unified system, enabling both classical and intuitionistic features, should shed some light not only on the logics themselves, but also in the ways they can interoperate. This in turn should help enhance the interoperability of proof assistants, to enable seamless communication between them, as discussed in the recent PhD thesis of Emilie Grienenberger, a student of under Gilles Dowek.
https://topos.institute/events/berkeley-seminar/")
![[Berkeley Seminar] Corinthia Aberlé | Synthetic Mathematics, Logical Frameworks, Categorical Algebra](https://i.ytimg.com/vi/MjkWT6GkISI/mqdefault.jpg "[Berkeley Seminar] Corinthia Aberlé | Synthetic Mathematics, Logical Frameworks, Categorical Algebra
Title: Synthetic Mathematics, Logical Frameworks, and Categorical Algebra
Abstract: I’ll be talking about three topics near and dear to my heart: synthetic mathematics, interactive theorem proving, and categorical algebra. My aim is to give an overview of how these topics are intimately linked, culminating in a discussion of how they can be used in tandem to give an elegant formal approach to problems at the heart of formal logic and type theory. To this end, I will proceed through a series of questions:
What is synthetic mathematics? …and why should I care?
What is a logical framework? …and how can I use one to help me do math?
What is categorical algebra? …and what are its limits?
What do synthetic mathematics, logical frameworks, and categorical algebra have to do with each other?
Date: 2025-07-01
https://topos.institute/events/berkeley-seminar/")
![[2-torial] Tim tells Jason about Deformation Theory [1/3]](https://i.ytimg.com/vi/MoBTZNGIjLs/mqdefault.jpg "[2-torial] Tim tells Jason about Deformation Theory [1/3]
[2-torial] Tim tells Jason about Deformation Theory [1/3]")
![[2-torial] Joanna tells Jason about enhanced simplicial categories](https://i.ytimg.com/vi/N04GYP5Qv7Y/mqdefault.jpg "[2-torial] Joanna tells Jason about enhanced simplicial categories
[2-torial] Joanna tells Jason about enhanced simplicial categories")
![[Berkeley Seminar] Shaowei Lin | Safety by Shared Synthesis](https://i.ytimg.com/vi/N1qZhOU5OWo/mqdefault.jpg "[Berkeley Seminar] Shaowei Lin | Safety by Shared Synthesis
Title: Safety by Shared Synthesis
Abstract: Today, critical infrastructure is vulnerable to both malicious attacks and unintended failures, and these risks are expected to grow in the foreseeable future. Deploying formal verification (FV) across critical cyber physical systems would dramatically improve safety and security, but has historically been too costly to use outside the simplest or most critical subsystems. AI could allow widespread use of FV in years not decades, shifting cyber risks strongly in favor of defense. In this talk, I will outline our report with Atlas Computing on AI-enabled tools for scaling formal verification (https://atlascomputing.org/ai-assisted-fv-toolchain.pdf). I will also discuss some lessons that I learnt along the way, especially about shared synthesis - the collaborative construction of formal specifications, implementations and proofs.
https://topos.site/events/berkeley-seminar/")
![[Oxford Seminar] David Jaz Myers | Preservation of 2-algebraic structure by pseudo-functors](https://i.ytimg.com/vi/NIhGTjTPnlY/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | Preservation of 2-algebraic structure by pseudo-functors
Oxford Seminar, 31st of January 2025
If universal algebra is the study of sets equipped with the structure of some operations satisfying universally quantified equations, then 2-algebra is the study of *categories* equipped with the structure of some operations, some natural transformations between these operations, and some equations between these. Examples of 2-algebras include symmetric monoidal categories and categories with finite products. Just as the functorial semantics (due to Lawvere) for algebra lets us interpret algebraic theories in categories other than sets (so long as they have finite products), the functorial semantics for 2-algebra (due to Power, Lack, and others) lets us interpret 2-algebraic structure in 2-categories other than Cat. For example, instead of symmetric monoidal categories, we can consider symmetric monoidal double categories. Any strict 2-functor that preserves finite products will push forward 2-algebraic structure. But 2-functors are often only functorial up to coherent isomorphism. What 2-algebraic structure do such cartesian pseudo-functors preserve? In this talk, well ask the question and put forward an answer: so long as the 2-algebraic theory is *flexible*, in the sense that it only asks for equations between transformations and not between operations, then it will be preserved by cartesian pseudo-functors.")
![[Oxford Seminar] Mirco Giacobbe | Neural certificates](https://i.ytimg.com/vi/O9T1zHj1cAA/mqdefault.jpg "[Oxford Seminar] Mirco Giacobbe | Neural certificates
Oxford Seminar, 13th of March 2025
Model checking aims to derive rigorous proofs for the correctness of
systems and has traditionally relied on symbolic reasoning methods. In
this talk, I will argue that model checking can also be effectively
addressed using machine learning too. I will present a realm of
approaches for formal verification that leverage neural networks to
represent correctness certificates of systems, known as neural
certificates. This approach trains certificates from synthetic
executions of the system and then validates them using symbolic
reasoning techniques. Building upon the observation that checking a
correctness certificate is much simpler than finding one, and that
neural networks are an appropriate representation for such
certificates, this results in a machine learning approach to model
checking that is entirely unsupervised, formally sound, and practically
effective. I will demonstrate the principles and experimental results
of this approach in safety assurance of software, probabilistic
systems, and control.
About the speaker:
Mirco Giacobbe is an Associate Professor at the University of Birmingham. He previously held research positions at the University of Oxford and Fondazione Bruno Kessler, and obtained his PhD at the Institute and Science and Technology Austria. His research interests lie between formal methods and artificial intelligence, where he develops automatic techniques to assure that algorithmic systems are safe and trustworthy.")
