5,778 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
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Weighted Automata and Monadic Second Order Logic
Let S be a commutative semiring. M. Droste and P. Gastin have introduced in
2005 weighted monadic second order logic WMSOL with weights in S. They use a
syntactic fragment RMSOL of WMSOL to characterize word functions (power series)
recognizable by weighted automata, where the semantics of quantifiers is used
both as arithmetical operations and, in the boolean case, as quantification.
Already in 2001, B. Courcelle, J.Makowsky and U. Rotics have introduced a
formalism for graph parameters definable in Monadic Second order Logic, here
called MSOLEVAL with values in a ring R. Their framework can be easily adapted
to semirings S. This formalism clearly separates the logical part from the
arithmetical part and also applies to word functions.
In this paper we give two proofs that RMSOL and MSOLEVAL with values in S
have the same expressive power over words. One proof shows directly that
MSOLEVAL captures the functions recognizable by weighted automata. The other
proof shows how to translate the formalisms from one into the other.Comment: In Proceedings GandALF 2013, arXiv:1307.416
Efficient First-Order Temporal Logic for Infinite-State Systems
In this paper we consider the specification and verification of
infinite-state systems using temporal logic. In particular, we describe
parameterised systems using a new variety of first-order temporal logic that is
both powerful enough for this form of specification and tractable enough for
practical deductive verification. Importantly, the power of the temporal
language allows us to describe (and verify) asynchronous systems, communication
delays and more complex properties such as liveness and fairness properties.
These aspects appear difficult for many other approaches to infinite-state
verification.Comment: 16 pages, 2 figure
Architectures in parametric component-based systems: Qualitative and quantitative modelling
One of the key aspects in component-based design is specifying the software
architecture that characterizes the topology and the permissible interactions
of the components of a system. To achieve well-founded design there is need to
address both the qualitative and non-functional aspects of architectures. In
this paper we study the qualitative and quantitative formal modelling of
architectures applied on parametric component-based systems, that consist of an
unknown number of instances of each component. Specifically, we introduce an
extended propositional interaction logic and investigate its first-order level
which serves as a formal language for the interactions of parametric systems.
Our logics achieve to encode the execution order of interactions, which is a
main feature in several important architectures, as well as to model recursive
interactions. Moreover, we prove the decidability of equivalence,
satisfiability, and validity of first-order extended interaction logic
formulas, and provide several examples of formulas describing well-known
architectures. We show the robustness of our theory by effectively extending
our results for parametric weighted architectures. For this, we study the
weighted counterparts of our logics over a commutative semiring, and we apply
them for modelling the quantitative aspects of concrete architectures. Finally,
we prove that the equivalence problem of weighted first-order extended
interaction logic formulas is decidable in a large class of semirings, namely
the class (of subsemirings) of skew fields.Comment: 53 pages, 11 figure
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