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DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…

Semantic role labeling (SRL) identifies predicate-argument structure(s) in a given sentence. Although different languages have different argument annotations, polyglot training, the idea of training one model on multiple languages, has…

In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…

Deep reinforcement learning (DRL), through learning policies or values represented by neural networks, has successfully addressed many complex control problems. However, the neural networks introduced by DRL lack interpretability and…

We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a…

For supervised classification problems involving design, control, other practical purposes, users are not only interested in finding a highly accurate classifier, but they also demand that the obtained classifier be easily interpretable.…

Recurrent Neural Networks (RNN) are known as powerful models for handling sequential data, and especially widely utilized in various natural language processing tasks. In this paper, we propose Contextual Recurrent Units (CRU) for enhancing…

We present a novel algorithm that efficiently computes near-optimal deterministic policies for constrained reinforcement learning (CRL) problems. Our approach combines three key ideas: (1) value-demand augmentation, (2) action-space…

We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward…

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…

Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…

The appearance of strong CDCL-based propositional (SAT) solvers has greatly advanced several areas of automated reasoning (AR). One of the directions in AR is thus to apply SAT solvers to expressive formalisms such as first-order logic, for…

Non-iterative normal modal logics are defined by axioms of modal degree 1. In this paper we use calculations with normal forms to determine the set of all possible non-iterative normal modal logics, unimodal propositional extensions of K.…

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…

We investigate the problem of extracting rules, expressed in Horn logic, from neural network models. Our work is based on the exact learning model, in which a learner interacts with a teacher (the neural network model) via queries in order…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…

A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…

We study the problem of rewriting an ontology O1 expressed in a DL L1 into an ontology O2 in a Horn DL L2 such that O1 and O2 are equisatisfiable when extended with an arbitrary dataset. Ontologies that admit such rewritings are amenable to…