2,214 research outputs found
Modal logics are coalgebraic
Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility
Relational Semantics of Non-Deterministic Dataflow
We recast dataflow in a modern categorical light using profunctors as a generalization of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preservemuch of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially theusual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higher-order dataflow as a biproduct,essentially by following the geometry of interaction programme
Typed linear algebra for weighted (probabilistic) automata
There is a need for a language able to reconcile the recent upsurge of interest in quantitative methods in the software sciences with logic and set theory that have been used for so many years in capturing the qualitative aspects of the same body of knowledge. Such a lingua franca should be typed, polymorphic, diagrammatic, calculational and easy to blend with traditional notation.
This paper puts forward typed linear algebra (LA) as a candidate notation for such a role. Typed LA emerges from regarding matrices as morphisms of suitable categories whereby traditional linear algebra is equipped with a type system.
In this paper we show typed LA at work in describing weighted (prob- abilistic) automata. Some attention is paid to the interface between the index-free language of matrix combinators and the corresponding index- wise notation, so as to blend with traditional set theoretic notation.Fundação para a Ciência e a Tecnologia (FCT
Clafer: Lightweight Modeling of Structure, Behaviour, and Variability
Embedded software is growing fast in size and complexity, leading to intimate
mixture of complex architectures and complex control. Consequently, software
specification requires modeling both structures and behaviour of systems.
Unfortunately, existing languages do not integrate these aspects well, usually
prioritizing one of them. It is common to develop a separate language for each
of these facets. In this paper, we contribute Clafer: a small language that
attempts to tackle this challenge. It combines rich structural modeling with
state of the art behavioural formalisms. We are not aware of any other modeling
language that seamlessly combines these facets common to system and software
modeling. We show how Clafer, in a single unified syntax and semantics, allows
capturing feature models (variability), component models, discrete control
models (automata) and variability encompassing all these aspects. The language
is built on top of first order logic with quantifiers over basic entities (for
modeling structures) combined with linear temporal logic (for modeling
behaviour). On top of this semantic foundation we build a simple but expressive
syntax, enriched with carefully selected syntactic expansions that cover
hierarchical modeling, associations, automata, scenarios, and Dwyer's property
patterns. We evaluate Clafer using a power window case study, and comparing it
against other notations that substantially overlap with its scope (SysML, AADL,
Temporal OCL and Live Sequence Charts), discussing benefits and perils of using
a single notation for the purpose
Relational Semantics of Linear Logic and Higher-order Model Checking
In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church encoding of any higher-order recursion scheme (HORS) comes together with a dual Church encoding of an alternating tree automata (ATA) of the same signature. Moreover, the interaction between the relational interpretations of the HORS and of the ATA identifies the set of accepting states of the tree automaton against the infinite tree generated by the recursion scheme. We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities) in higher-order model-checking. We show in particular how to reunderstand in this way the type-theoretic approach to higher-order model-checking developed by Kobayashi and Ong. We briefly explain in the end of the paper how this analysis driven by linear logic results in a new and purely semantic proof of decidability of the formulas of the monadic second-order logic for higher-order recursion schemes
Bisimilarity is not Borel
We prove that the relation of bisimilarity between countable labelled
transition systems is -complete (hence not Borel), by reducing the
set of non-wellorders over the natural numbers continuously to it.
This has an impact on the theory of probabilistic and nondeterministic
processes over uncountable spaces, since logical characterizations of
bisimilarity (as, for instance, those based on the unique structure theorem for
analytic spaces) require a countable logic whose formulas have measurable
semantics. Our reduction shows that such a logic does not exist in the case of
image-infinite processes.Comment: 20 pages, 1 figure; proof of Sigma_1^1 completeness added with
extended comments. I acknowledge careful reading by the referees. Major
changes in Introduction, Conclusion, and motivation for NLMP. Proof for Lemma
22 added, simpler proofs for Lemma 17 and Theorem 30. Added references. Part
of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logic
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