Related papers: Graded Monads and Graded Logics for the Linear Tim…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
In Linear Logic ($\mathsf{LL}$), the exponential modality $!$ brings forth a distinction between non-linear proofs and linear proofs, where linear means using an argument exactly once. Differential Linear Logic ($\mathsf{DiLL}$) is an…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is…
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…
First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
We present a library-level formalisation of Hennessy-Milner Logic (HML) - a foundational logic for labelled transition systems (LTSs) - for the Lean Computer Science Library (CSLib). Our development includes the syntax, satisfaction…
Often fairness assumptions need to be made in order to establish liveness properties of distributed systems, but in many situations they lead to false conclusions. This document presents a research agenda aiming at laying the foundations of…
We introduce cut-free nested sequent systems for a broad class of quantified modal logics (QMLs). The QMLs we consider are semantically defined using relational models that assign both an inner and outer domain to each world. This rich…
Process equivalences are formal methods that relate programs and system which, informally, behave in the same way. Since there is no unique notion of what it means for two dynamic systems to display the same behaviour there are a multitude…
This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labelled transition systems, and formats of transition system specifications using Plotkin's…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
For the advancements of time series classification, scrutinizing previous studies, most existing methods adopt a common learning-to-classify paradigm - a time series classifier model tries to learn the relation between sequence inputs and…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model…
Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
We propose behavioral specification theories for most equivalences in the linear-time--branching-time spectrum. Almost all previous work on specification theories focuses on bisimilarity, but there is a clear interest in specification…