Related papers: Temporal Type Theory: A topos-theoretic approach t…
Large Language Models (LLMs) are increasingly deployed as autonomous agents capable of reasoning, planning, and acting within interactive environments. Despite their growing capability to perform multi-step reasoning and decision-making…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
We investigate the extent to which Linear Temporal Logic (LTL) formulas can be uniquely characterized by a finite set of labeled examples. We consider different types of examples, ranging from finite words to transfinite words, as well as…
Theory of Mind (ToM)-the cognitive ability to reason about mental states of ourselves and others, is the foundation of social interaction. Although ToM comes naturally to humans, it poses a significant challenge to even the most advanced…
Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as networks of telecommunication, neural signal processing, biochemical reactions and human…
As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena…
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved…
Temporal predictive models have the potential to improve decisions in health care, public services, and other domains, yet they often fail to effectively support decision-makers. Prior literature shows that many misalignments between model…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
In the field of Learning from Demonstration (LfD), enabling robots to generalize learned manipulation skills to novel scenarios for long-horizon tasks remains challenging. Specifically, it is still difficult for robots to adapt the learned…
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
Everyday conversations require understanding everyday events, which in turn, requires understanding temporal commonsense concepts interwoven with those events. Despite recent progress with massive pre-trained language models (LMs) such as…
We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…
Our aim is to investigate ontology-based data access over temporal data with validity time and ontologies capable of temporal conceptual modelling. To this end, we design a temporal description logic, TQL, that extends the standard ontology…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
It is proposed that the theory of dynamical systems offers appropriate tools to model many phonological aspects of both speech production and perception. A dynamic account of speech rhythm is shown to be useful for description of both…