Related papers: Foundational Extensible Corecursion
The birth of Foundation Models brought unprecedented results in a wide range of tasks, from language to vision, to robotic control. These models are able to process huge quantities of data, and can extract and develop rich representations,…
Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE…
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
We formulate sequential maximum a posteriori inference as a recursion of loss functions and reduce the problem of continual learning to approximating the previous loss function. We then propose two coreset-free methods: autodiff quadratic…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…
This paper introduces a new method for redefining the Roman factorial using universally applicable functions that are not expressed in closed form. We present a set of foundational functions, similar to Boolean operations, to simplify the…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive…
We describe a design-based framework for drawing causal inference in general randomized experiments. Causal effects are defined as linear functionals evaluated at unit-level potential outcome functions. Assumptions about the potential…
With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We define a novel calculus that combines a call-by-name functional core with session-based communication primitives. We develop a typing discipline that guarantees both normalisation of expressions and progress of processes and that…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have…
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…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…