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Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It…
We present quantitative probing as a model-agnostic framework for validating causal models in the presence of quantitative domain knowledge. The method is constructed as an analogue of the train/test split in correlation-based machine…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
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…
We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…
Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
We propose a categorical framework for linear-time temporal verification of effectful higher-order programs, including probabilistic higher-order programs. Our framework provides a generic denotational reduction -- namely, a denotational…
This paper addresses the fundamental question of determining the minimum number of distinct control laws required for global controllability of nonlinear systems that exhibit singularities in their feedback linearising controllers. We…
Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
We introduce a data-driven approach to computing finite bisimulations for state transition systems with very large, possibly infinite state space. Our novel technique computes stutter-insensitive bisimulations of deterministic systems,…
Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
The increasing use of machine learning in practice and legal regulations like EU's GDPR cause the necessity to be able to explain the prediction and behavior of machine learning models. A prominent example of particularly intuitive…
Uncertainty quantification of complex technical systems is often based on a computer model of the system. As all models such a computer model is always wrong in the sense that it does not describe the reality perfectly. The purpose of this…