Related papers: Beyond the Elementary Representations of Program I…
Neural language models (LMs) perform well on tasks that require sensitivity to syntactic structure. Drawing on the syntactic priming paradigm from psycholinguistics, we propose a novel technique to analyze the representations that enable…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…
Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being…
The purpose of this paper is to use reinforcement learning to model learning agents which can recognize formal languages. Agents are modeled as simple multi-head automaton, a new model of finite automaton that uses multiple heads, and six…
The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or…
We consider the problem of computing optimal generalised policies for relational Markov decision processes. We describe an approach combining some of the benefits of purely inductive techniques with those of symbolic dynamic programming…
In a recent paper by Harrison et al., the concept of program completion is extended to a large class of programs in the input language of the ASP grounder gringo. We would like to automate the process of generating and simplifying…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed, using an abstract…
Finding preferences expressed in natural language is an important but challenging task. State-of-the-art(SotA) methods leverage transformer-based models such as BERT, RoBERTa, etc. and graph neural architectures such as graph attention…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…
Large Language Models (LLMs) have emerged as powerful tools for accelerating scientific discovery, yet their static knowledge and hallucination issues hinder autonomous research applications. Recent advances integrate LLMs into agentic…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
Classical planning representation languages based on first-order logic have preliminarily been used to model and solve robotic task planning problems. Wider adoption of these representation languages, however, is hindered by the limitations…
A representation invariant is a property that holds of all values of abstract type produced by a module. Representation invariants play important roles in software engineering and program verification. In this paper, we develop a…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge…