skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: SEMI-EQUATIONAL THEORIES
Abstract We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.  more » « less
Award ID(s):
1651321
PAR ID:
10441603
Author(s) / Creator(s):
;
Date Published:
Journal Name:
The Journal of Symbolic Logic
ISSN:
0022-4812
Page Range / eLocation ID:
1 to 32
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Endrullis, Jörg; Schmitz, Sylvain (Ed.)
    We prove that the equational theory of Kleene algebra with commutativity conditions on primitives (or atomic terms) is undecidable, thereby settling a longstanding open question in the theory of Kleene algebra. While this question has also been recently solved independently by Kuznetsov, our results hold even for weaker theories that do not support the induction axioms of Kleene algebra. 
    more » « less
  2. ; ; (, Journal of High Energy Physics)
    A bstract In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to leading order in the t’Hooft coupling and 1/ N . We found that in this limit, the Lyapunov exponent remains comparable in magnitude to (and somewhat smaller than) the exponent in the commutative case. This can possibly be explained by the infrared sensitivity of the Lyapunov exponent. Another possible explanation is that in examples of weakly coupled non-commutative field theories, non-local contributions to various thermodynamic quantities are sub-dominant. 
    more » « less
  3. ; ; ; (, International Conference on Learning Representations (ICLR))
    Semi-supervised learning and weakly supervised learning are important paradigms that aim to reduce the growing demand for labeled data in current machine learning applications. In this paper, we introduce a novel analysis of the classical label propagation algorithm (LPA) (Zhu & Ghahramani, 2002) that moreover takes advantage of useful prior information, specifically probabilistic hypothesized labels on the unlabeled data. We provide an error bound that exploits both the local geometric properties of the underlying graph and the quality of the prior information. We also propose a framework to incorporate multiple sources of noisy information. In particular, we consider the setting of weak supervision, where our sources of information are weak labelers. We demonstrate the ability of our approach on multiple benchmark weakly supervised classification tasks, showing improvements upon existing semi-supervised and weakly supervised methods. 
    more » « less
  4. ; (, Proceedings of the ACM on Programming Languages)
    Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by uninterpreted events, while admitting a rich equational theory of equivalence. But monads are not the only way to structure effectful computation, why should we limit ourselves? In this paper, inspired by applicative functors, selective functors, and other structures, we define a collection of data structures and theories, which we call program adverbs, that capture a variety of computational patterns. Program adverbs are themselves composable, allowing them to be used to specify the semantics of languages with multiple computation patterns. We use program adverbs as the basis for a new class of semantic embeddings called Tlön embeddings. Compared with embeddings based on free monads, Tlön embeddings allow more flexibility in computational modeling of effects, while retaining more information about the program's syntactic structure. 
    more » « less
  5. ; ; ; (, Journal of High Energy Physics)
    A bstract We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the S-matrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email