Related papers: Nested Sequents for Horn-Characterizable Quantifie…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
Contextual embeddings represent a new generation of semantic representations learned from Neural Language Modelling (NLM) that addresses the issue of meaning conflation hampering traditional word embeddings. In this work, we show that…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
We say that a Kripke model is a GL-model if the accessibility relation $\prec$ is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by attaching infinitely many worlds $t_1, t_2, \ldots$, and…
We present a proof system for the provability logic GLP in the formalism of nested sequents and prove the cut elimination theorem for it. As an application, we obtain the reduction of GLP to its important fragment called J syntactically.
In this paper, we propose a sequential neural encoder with latent structured description (SNELSD) for modeling sentences. This model introduces latent chunk-level representations into conventional sequential neural encoders, i.e., recurrent…
This work is concerned with the fundamental scaling laws of quasi-complementary sequence sets (QCSSs) by understanding how large the set size (denoted by $M$) can grow with the flock size ($K$) and the sequence length ($N$). We first…
Data-aware modal logics offer a powerful formalism for reasoning about semi-structured queries in languages such as DataGL, XPath, and GQL. In brief, these logics can be viewed as modal systems capable of expressing both reachability…
Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition…
The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable…
We propose Fluid Logic, a paradigm in which modal logical reasoning, temporal, epistemic, doxastic, deontic, is lifted from discrete Kripke structures to continuous manifolds via Neural Stochastic Differential Equations (Neural SDEs). Each…
We introduce labelled sequent calculi for quantified modal logics with definite descriptions. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible,…
We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…
Default logic encounters some conceptual difficulties in representing common sense reasoning tasks. We argue that we should not try to formulate modular default rules that are presumed to work in all or most circumstances. We need to take…
The identification of syllables within phonetic sequences is known as syllabification. This task is thought to play an important role in natural language understanding, speech production, and the development of speech recognition systems.…