Declarative operations on nets

To increase the expressiveness of knowledge representations, the graph-theoretical basis of semantic networks is reconsidered. Directed labeled graphs are generalized to directed recursive labelnode hypergraphs, which permit a most natural representation of multi-level structures and n-ary relationships. This net formalism is embedded into the relational/functional programming language RELFUN. Operations on (generalized) graphs are specified in a declarative fashion to enhance readability and maintainability. For this, nets are represented as nested RELFUN terms kept in a normal form by rules associated directly with their constructors. These rules rely on equational axioms postulated in the formal definition of the generalized graphs as a constructor algebra. Certain kinds of sharing in net diagrams are mirrored by binding common subterms to logical variables. A package of declarative transformations on net terms is developed. It includes generalized set operations, structure-reducing operations, and extended path searching. The generation of parts lists is given as an application in mechanical engineering. Finally, imperative net storage and retrieval operations are discussed

From Word Models to World Models: Translating from Natural Language to the Probabilistic Language of Thought

How does language inform our downstream thinking? In particular, how do humans make meaning from language -- and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose \textit{rational meaning construction}, a computational framework for language-informed thinking that combines neural models of language with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a \textit{probabilistic language of thought} (PLoT) -- a general-purpose symbolic substrate for probabilistic, generative world modeling. Our architecture integrates two powerful computational tools that have not previously come together: we model thinking with \textit{probabilistic programs}, an expressive representation for flexible commonsense reasoning; and we model meaning construction with \textit{large language models} (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework in action through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning about agents and their plans. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves

Higher-Order Calculations in Quantum Chromodynamics

In this thesis, several techniques and advances in higher-order Quantum Chromodynamics (QCD) calculations are presented. There is a particular focus on 2-loop 5-point massless QCD amplitudes, which are currently at the frontier of higher-order QCD calculations. Firstly, we study the Brodsky-Lepage-Mackenzie/Principle of Maximum Conformality (BLM/PMC) method for setting the renormalisation scale, μ_R, in higher-order QCD calculations. We identify three ambiguities in the BLM/PMC procedure and study their numerical impact using the example of the total cross-section for top-pair production at Next-to-Next-to-Leading Order (NNLO) in QCD. The numerical impact of these ambiguities on the BLM/PMC prediction for the cross-section is found to be comparable to the impact of the choice of μ_R in the conventional scale-setting approach. Secondly, we introduce a novel strategy for solving integration-by-parts (IBP) identities, which are widely used in the computation of multi-loop QCD amplitudes. We implement the strategy in an efficient C++ program and hence solve the IBP identities needed for the computation of any planar 2-loop 5-point massless amplitude in QCD. We also derive representative results for the most complicated non-planar family of integrals. Thirdly, we present an automated computational framework to reduce 2-loop 5-point massless amplitudes to a basis of pentagon functions. It uses finite-field evaluation and interpolation techniques, as well as the aforementioned analytical IBP results. We use this to calculate the leading-colour 2-loop QCD amplitude for qq̄→γγγ and then compute the NNLO QCD corrections to 3-photon production at the LHC. This is the first NNLO QCD calculation for a 2→3 process. We compare our predictions with the available 8 TeV measurements from the ATLAS collaboration and we find that the inclusion of the NNLO corrections eliminates the existing significant discrepancy with respect to NLO QCD predictions, paving the way for precision phenomenology in this process

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems