Related papers: Structural Refinement for the Modal nu-Calculus
Contextual refinement (CR) is one of the standard notions of specifying open programs. CR has two main advantages: (i) (horizontal and vertical) compositionality that allows us to decompose a large contextual refinement into many smaller…
We present assume-guarantee contracts for continuous-time linear dynamical systems with inputs and outputs. These contracts are used to express specifications on the dynamic behaviour of a system. Contrary to existing approaches, we use…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an…
In recent years, great progress has been made in the field of formal verification for low-level systems. Many of them are based on one of two popular approaches: refinement or unary separation logic. These two approaches are very different…
We present a metagrammatical formalism, {\em generic rules}, to give a default interpretation to grammar rules. Our formalism introduces a process of {\em dynamic binding} interfacing the level of pure grammatical knowledge representation…
We consider the setting of component-based design for real-time systems with critical timing constraints. Based on our earlier work, we propose a compositional specification theory for timed automata with I/O distinction, which supports…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria,…
For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable…
The paper explores properties of the {\L}ukasiewicz {\mu}-calculus, or {\L}{\mu} for short, an extension of {\L}ukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…
Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…