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Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Feature Structures (FSs) are a widespread tool used for decompositional frameworks of Attribute-Value associations. Even though they thrive in simple systems, they lack a way of representing higher-order entities and relations. This is…
Modeling the complex interactions between users and items as well as amongst items themselves is at the core of designing successful recommender systems. One classical setting is predicting users' personalized sequential behavior (or…
The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our…
In this paper, we present a new technique for studying the dynamics of a finitely generated rational semigroup. Such a semigroup can be associated naturally to a certain holomorphic correspondence on $\mathbb{P}^1$. Then, results on the…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure…
We give Hennessy-Milner classes for intuitionistic, dual-intuitionistic and bi-intuitionistic logic interpreted in intuitionistic Kripke models, and generalise these results to modal (dual- and bi-)intuitionistic logics. Our main technical…
First-order relational languages have been used in MDP planning and reinforcement learning (RL) for two main purposes: specifying MDPs in compact form, and representing and learning policies that are general and not tied to specific…
One of the consequences of the Compactness Principle in structural Ramsey theory is that the small Ramsey degrees cannot exceed the corresponding big Ramsey degrees, thereby justifying the choice of adjectives. However, it is unclear what…
In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
We present a family of minimal modal logics (namely, modal logics based on minimal propositional logic) corresponding each to a different classical modal logic. The minimal modal logics are defined based on their classical counterparts in…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…
We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded by two coupled channels-drift and diffusion-whose algebraic…
This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation. We focus on showing…