Related papers: Coinduction up to in a fibrational setting
The Circularity Principle was successfully applied for developing a coinductive proving technique, known as circular coinduction. In this paper, we show that the same principle can be used to develop an inductive proving technique. A main…
Motivated by applications in modelling quantum systems using coalgebraic techniques, we introduce a fibred coalgebraic logic. Our approach extends the conventional predicate lifting semantics with additional modalities relating conditions…
Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic…
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the…
This paper shows that guarded systems of recursive equations have unique solutions up to strong bisimilarity for any process algebra with a structural operation semantics in the ready simulation format. A similar result holds for simulation…
Bisimulation metric is a robust behavioural semantics for probabilistic processes. Given any SOS specification of probabilistic processes, we provide a method to compute for each operator of the language its respective metric…
We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
Many concurrent and distributed systems are safety-critical and therefore have to provide a high degree of assurance. Important properties of such systems are frequently proved on the specification level, but implementations typically…
In top-down multi-level design methodologies, design descriptions at higher levels of abstraction are incrementally refined to the final realizations. Simulation based techniques have traditionally been used to verify that such model…
Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that…
Many properties of communication protocols combine safety and liveness aspects. Characterizing such combined properties by means of a single inference system is difficult because of the fundamentally different techniques (coinduction and…
The topic of provable deep neural network robustness has raised considerable interest in recent years. Most research has focused on adversarial robustness, which studies the robustness of perceptive models in the neighbourhood of particular…
Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The…
There exists a rich literature of rule formats guaranteeing different algebraic properties for formalisms with a Structural Operational Semantics. Moreover, there exist a few approaches for automatically deriving axiomatizations…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
In this paper we study strong and weak bisimulation equivalences for continuous-time Markov decision processes (CTMDPs) and the logical characterizations of these relations with respect to the continuous-time stochastic logic (CSL). For…
Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic…