10 citations · 16 across the 17 of their papers we have counts for
23 papers
The Only Distributive Law Over the Powerset Monad Is the One You Know
Sergey Goncharov, Dirk Hofmann, Pedro Nora +2
Distributive laws of set functors over the powerset monad (also known as Kleisli laws for the powerset monad) are well-known to be in one-to-one correspondence with extensions of s…
Computing Distinguishing Formulae for Threshold-Based Behavioural Distances
Jonas Forster, Lutz Schröder, Paul Wild +2
Behavioural distances generally offer more fine-grained means of comparing quantitative systems than two-valued behavioural equivalences. They often relate to quantitative modaliti…
Generalized Kantorovich-Rubinstein Duality beyond Hausdorff and Kantorovich
Paul Wild, Lutz Schröder, Karla Messing +2
The classical Kantorovich-Rubinstein duality guarantees coincidence between metrics on the space of probability distributions defined on the one hand via transport plans (couplings…
Non-Expansive Fuzzy Coalgebraic Logic
Stefan Gebhart, Lutz Schröder, Paul Wild
Fuzzy logic extends the classical truth values "true" and "false" with additional truth degrees in between. More specifically, fuzzy modal logics in this sense are given by a choic…
Non-expansive Fuzzy ALC
Stefan Gebhart, Lutz Schröder, Paul Wild
Fuzzy description logics serve the representation of vague knowledge, typically letting concepts take truth degrees in the unit interval. Expressiveness, logical properties, and co…
Relators and Notions of Simulation Revisited
Sergey Goncharov, Dirk Hofmann, Pedro Nora +2
Simulations and bisimulations are ubiquitous in the study of concurrent systems and modal logics of various types. Besides classical relational transition systems, relevant system…
Behavioural Conformances based on Lax Couplings
Paul Wild, Lutz Schröder
Behavioural conformances -- e.g. behavioural equivalences, distances, preorders -- on a wide range of system types (non-deterministic, probabilistic, weighted etc.) can be dealt wi…
Conformance Games for Graded Semantics
Jonas Forster, Lutz Schröder, Paul Wild
Game-theoretic characterizations of process equivalences traditionally form a central topic in concurrency; for example, most equivalences on the classical linear-time / branching-…
Relational Connectors and Heterogeneous Bisimulations
Pedro Nora, Jurriaan Rot, Lutz Schröder +1
While behavioural equivalences among systems of the same type, such as Park/Milner bisimilarity of labelled transition systems, are an established notion, a systematic treatment of…
Identity-Preserving Lax Extensions and Where to Find Them
Sergey Goncharov, Dirk Hofmaan, Pedro Nora +2
Generic notions of bisimulation for various types of systems (nondeterministic, probabilistic, weighted etc.) rely on identity-preserving (normal) lax extensions of the functor enc…
Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques
Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss +4
Behavioural distances of transition systems modelled via coalgebras for endofunctors generalize traditional notions of behavioural equivalence to a quantitative setting, in which s…
Expressive Quantale-valued Logics for Coalgebras: an Adjunction-based Approach
Harsh Beohar, Sebastian Gurke, Barbara König +4
We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on earlie…
Graded Semantics and Graded Logics for Eilenberg-Moore Coalgebras
Jonas Forster, Lutz Schröder, Paul Wild +3
Coalgebra, as the abstract study of state-based systems, comes naturally equipped with a notion of behavioural equivalence that identifies states exhibiting the same behaviour. In…
Quantitative Graded Semantics and Spectra of Behavioural Metrics
Jonas Forster, Lutz Schröder, Paul Wild +4
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition…
The feet of orthogonal Buekenhout-Metz unitals
S. G. Barwick, W. -A. Jackson, P. Wild
In this article we look at the geometric structure of the feet of an orthogonal Buekenhout-Metz unital U in PG(2,q^2). We show that the feet of each point form a set of type (0,1,2…
Quantitative Hennessy-Milner Theorems via Notions of Density
Jonas Forster, Sergey Goncharov, Dirk Hofmann +3
The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled t…
Kantorovich Functors and Characteristic Logics for Behavioural Distances
Sergey Goncharov, Dirk Hofmann, Pedro Nora +2
Behavioural distances measure the deviation between states in quantitative systems, such as probabilistic or weighted systems. There is growing interest in generic approaches to be…
A Point-free Perspective on Lax extensions and Predicate liftings
Sergey Goncharov, Dirk Hofmann, Pedro Nora +2
Lax extensions of set functors play a key role in various areas including topology, concurrent systems, and modal logic, while predicate liftings provide a generic semantics of mod…
Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions
Paul Wild, Lutz Schröder
In systems involving quantitative data, such as probabilistic, fuzzy, or metric systems, behavioural distances provide a more fine-grained comparison of states than two-valued noti…
A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic
Paul Wild, Lutz Schröder, Dirk Pattinson +1
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under pr…
A van Benthem Theorem for Quantitative Probabilistic Modal Logic
Paul Wild, Lutz Schröder, Dirk Pattinson +1
In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate str…
A van Benthem Theorem for Fuzzy Modal Logic
Paul Wild, Lutz Schröder, Dirk Pattinson +1
We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic.…
A Characterization Theorem for a Modal Description Logic
Paul Wild, Lutz Schröder
Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combi…