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Modal and guarded characterisation theorems over finite transition systems
2004
Annals of Pure and Applied Logic
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We explore the finite model theory of the characterisation theorems for modal and guarded fragments of first-order logic over transition systems and relational structures of width two. ...
These techniques are used to prove several ramifications of the van Benthem-Rosen characterisation theorem of basic modal logic for refinements of ordinary bisimulation equivalence, both in the sense of ...
This research was partially supported by EPSRC grant GR/R11896/01, and by a Royal Society European Joint Project grant. ...
doi:10.1016/j.apal.2004.04.003
fatcat:mbtw7eh4njdztn7hnix6usdeae
Modal and guarded characterisation theorems over finite transition systems
Proceedings 17th Annual IEEE Symposium on Logic in Computer Science
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We explore the finite model theory of the characterisation theorems for modal and guarded fragments of first-order logic over transition systems and relational structures of width two. ...
These techniques are used to prove several ramifications of the van Benthem-Rosen characterisation theorem of basic modal logic for refinements of ordinary bisimulation equivalence, both in the sense of ...
This research was partially supported by EPSRC grant GR/R11896/01, and by a Royal Society European Joint Project grant. ...
doi:10.1109/lics.2002.1029844
dblp:conf/lics/Otto02
fatcat:vxzgfj5iqrdlpjisot7xao6rdy
The Freedoms of (Guarded) Bisimulation
[chapter]
2014
Outstanding Contributions to Logic
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Yet modal logics, transition systems and game graphs bridge the apparent gap in a natural manner and typically allow us to understand behavioural comparisons ...
Typically such characterisation theorems state that a modal or guarded logic is not only invariant under bisimulation but, conversely, also expressively complete for the class of all bisimulation invariant ...
Theorem 1.2 (Ehrenfeucht-Fraïssé and Karp theorems for ML) In restriction to finite modal vocabularies, and for every ∈ N: A, a ∼ B, b if, and only if, A, a ≡ ML B, b. ...
doi:10.1007/978-3-319-06025-5_1
fatcat:mi4q4wbo65fepnxvrbrafxcwxu
Bisimulation Invariant Monadic-Second Order Logic in the Finite
2018
International Colloquium on Automata, Languages and Programming
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We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. ...
In particular, we show that, over the class of all finite transition systems with Cantor-Bendixson rank at most k, bisimulation-invariant MSO coincides with L µ . ...
Theorem 2.8. Over every finite class C of finite transition systems, bisimulation-invariant MSO coincides with L µ . ...
doi:10.4230/lipics.icalp.2018.117
dblp:conf/icalp/BlumensathW18
fatcat:x5jxvqdl7bg3rfiyu2ixsqmwu4
Bisimulation and Coverings for Graphs and Hypergraphs
[chapter]
2013
Lecture Notes in Computer Science
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We survey notions of bisimulation and of bisimilar coverings both in the world of graph-like structures (Kripke structures, transition systems) and in the world of hypergraph-like general relational structures ...
The provision of finite analogues for full infinite tree-like unfoldings, in particular, raises interesting combinatorial challenges and is the key to a number of interesting model-theoretic applications ...
modal context in the analysis of transition systems and graph-like structures, cf ...
doi:10.1007/978-3-642-36039-8_2
fatcat:y5ycwkiqubbtpdouj7fnjxo3pa
Author Index
2004
Annals of Pure and Applied Logic
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-H.L., An approach to deciding the observational equivalence of Algol-like languages (1-3) 125-171 Otto, M., Modal and guarded characterisation theorems over finite transition systems (1-3) 173-205 Plotkin ...
term rewriting systems in polynomial time (1-3) 33-59 Grohe, M., see Frick, M. ...
doi:10.1016/s0168-0072(04)00115-0
fatcat:uvctnxmfzzddfeuo3fyozfjm3q
Bisimulation Invariant Monadic-Second Order Logic in the Finite
[article]
2019
arXiv
pre-print
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We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. ...
In particular, we show that, over the class of all finite transition systems with Cantor-Bendixson rank at most k, bisimulation-invariant MSO coincides with L_mu. ...
that is bisimulation-invariant over the class of all finite transition systems is equivalent, over that class, to the corresponding modal logic. ...
arXiv:1905.06668v1
fatcat:cc4i7ivxyzfnbkhwgp2ltu4ok4
Deciding properties of regular real timed processes
[chapter]
1992
Lecture Notes in Computer Science
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Two operational semantics, and associated timed notions of bisimulation, are given: a standard infinite semantics, and a symbolic finite semantics. ...
In these models the addition of time does not contribute to the infiniteness of the labelled transition system in terms of which the the operational semantics of processes is given. ...
Extended Timed Modal Logic In this section we introduce an extension of TML where the quantification over action-transitions and time--transitions has been separated. ...
doi:10.1007/3-540-55179-4_41
fatcat:jl26vef7jvgzhhn4cb5lwrfbgi
1 Modal logic: a semantic perspective
[chapter]
2007
Studies in Logic and Practical Reasoning
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How does modal logic compare with these logics as a tool for talking about graphs? Can modal expressivity over graphs be characterised in terms of classical logic? ...
In Section 2, we introduce basic modal languages and the graphs over which they are interpreted. ...
Different applications of modal logic typically validate different modal axioms -axioms over and above those to be found in the minimal system K. ...
doi:10.1016/s1570-2464(07)80004-8
fatcat:unpkk66lxjdibjbv4epdapt6yu
Expressive completeness through logically tractable models
2013
Annals of Pure and Applied Logic
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One new result concerns expressive completeness w.r.t. guarded negation bisimulation, a back-and-forth equivalence involving local homomorphisms. ...
We highlight some constructions involving degrees of acyclicity and saturation that can be achieved in finite model constructions, and discuss their uses towards expressive completeness w.r.t. bisimulation ...
I am grateful for discussions with Vince Bárány and Balder ten Cate concerning the guarded negation fragment. ...
doi:10.1016/j.apal.2013.06.017
fatcat:cj5cxfl2afhanouwu6l44j5z3m
A Modal Logic for Network Topologies
[chapter]
2000
Lecture Notes in Computer Science
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to describe and reason about the topologies of multi-agent systems. ...
We show that the language is semantically characterised by a generalisation of classical bisimulation, called history-based bisimulation, consider its decidability and study the application of the logic ...
Before we phrase the semantic characterisation of the language Ä ½ in theorem 15, we define the notion of an image finite state. ...
doi:10.1007/3-540-40006-0_19
fatcat:ogj3nnfp5jhqpbvgivrw2pp4zy
Compositional verification of sequential programs with procedures
2008
Information and Computation
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We present a novel maximal model construction for the fragment of the modal -calculus with boxes and greatest fixed points only, and adapt it to control-flow graphs modelling components described in a ...
Our compositional verification method builds on a technique proposed by Grumberg and Long that uses maximal models to reduce compositional verification of finite-state parallel processes to standard model ...
The extension of HML with greatest fixed points (or, equivalently, simulation logic with diamond modalities) requires more general models than modal transition systems: a finite maximal modal transition ...
doi:10.1016/j.ic.2008.03.003
fatcat:i2bb4ckl5ngp3aa6ezxzhpqt4a
EXPTIME Tableaux for the Coalgebraic μ-Calculus
[chapter]
2009
Lecture Notes in Computer Science
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The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics ...
and coalition logic. ...
Theorem 17. Let R be a one-step tableau complete set of monotone rules for the modal similarity type Λ, and let Γ ∈ S(Λ) be clean and guarded. ...
doi:10.1007/978-3-642-04027-6_15
fatcat:tdqe46nv6jdp3p6s2sfxu2tjpu
Sequent Calculus in the Topos of Trees
[article]
2015
arXiv
pre-print
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Nakano's "later" modality, inspired by Gödel-Löb provability logic, has been applied in type systems and program logics to capture guarded recursion. ...
Birkedal et al modelled this modality via the internal logic of the topos of trees. ...
Acknowledgments We gratefully acknowledge helpful discussions with Lars Birkedal, Stephané Demri, Tadeusz Litak, and Jimmy Thomson, and the comments of the reviewers of this and a previous unsuccessful ...
arXiv:1501.03293v2
fatcat:gjav5oyn3vbbnbo43xzx46o6yi
Sequent Calculus in the Topos of Trees
[chapter]
2015
Lecture Notes in Computer Science
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Nakano's "later" modality, inspired by Gödel-Löb provability logic, has been applied in type systems and program logics to capture guarded recursion. ...
and finite model property of these logics. ...
Acknowledgments We gratefully acknowledge helpful discussions with Lars Birkedal, Stephané Demri, Tadeusz Litak, and Jimmy Thomson, and the comments of the reviewers of this and a previous unsuccessful ...
doi:10.1007/978-3-662-46678-0_9
fatcat:hxn3oyxyf5dvzij4abuepbdrke
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