Related papers: The Syntax of the Accounting Language: A First Ste…
Solving algebra problems (APs) continues to attract significant research interest as evidenced by the large number of algorithms and theories proposed over the past decade. Despite these important research contributions, however, the body…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
Table annotation is crucial for making web and enterprise tables usable in downstream NLP applications. Unlike textual data where learning semantically rich token or sentence embeddings often suffice, tables are structured combinations of…
Reasoning about program equivalence in imperative languages is notoriously challenging, as the presence of states (in the form of variable stores) fundamentally increases the observational power of program terms. The key desideratum for any…
Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…
Current natural language systems designed for multi-step claim validation typically operate in two phases: retrieve a set of relevant premise statements using heuristics (planning), then generate novel conclusions from those statements…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
The goal of this thesis is to advance the exploration of the statistical language learning design space. In pursuit of that goal, the thesis makes two main theoretical contributions: (i) it identifies a new class of designs by specifying an…
Table entailment, the binary classification task of finding if a sentence is supported or refuted by the content of a table, requires parsing language and table structure as well as numerical and discrete reasoning. While there is extensive…
The present paper contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update…
We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…
In a seminal work, K. Segerberg introduced a deontic logic called DAL to investigate normative reasoning over actions. DAL marked the beginning of a new area of research in Deontic Logic by shifting the focus from deontic operators on…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…
Opetopes are algebraic descriptions of shapes corresponding to compositions in higher dimensions. As such, they offer an approach to higher-dimensional algebraic structures, and in particular, to the definition of weak $\omega$-categories,…
We present nested sequent systems for propositional G\"odel-Dummett logic and its first-order extensions with non-constant and constant domains, built atop nested calculi for intuitionistic logics. To obtain nested systems for these…