Related papers: Some observations on the logical foundations of in…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Recent advances in automated theorem proving use Large Language Models (LLMs) to translate informal mathematical statements into formal proofs. However, informal cues are often ambiguous or lack strict logical structure, making it hard for…
Interpretability is an elusive but highly sought-after characteristic of modern machine learning methods. Recent work has focused on interpretability via $\textit{explanations}$, which justify individual model predictions. In this work, we…
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
Despite its great success, machine learning can have its limits when dealing with insufficient training data. A potential solution is the additional integration of prior knowledge into the training process which leads to the notion of…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an…
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Since language models are used to model a wide variety of languages, it is natural to ask whether the neural architectures used for the task have inductive biases towards modeling particular types of languages. Investigation of these biases…
I introduce an approach for automated reasoning in first order set theories that are not finitely axiomatizable, such as $ZFC$, and describe its implementation alongside the automated theorem proving software E. I then compare the results…
In Feferman's work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin-Lof type theory and constructive Zermelo-Fraenkel set…