Filters








673 Hits in 6.7 sec

Modal and guarded characterisation theorems over finite transition systems

Martin Otto
2004 Annals of Pure and Applied Logic  
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

M. Otto
Proceedings 17th Annual IEEE Symposium on Logic in Computer Science  
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]

Erich Grädel, Martin Otto
2014 Outstanding Contributions to Logic  
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

Achim Blumensath, Felix Wolf, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
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]

Martin Otto
2013 Lecture Notes in Computer Science  
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  
-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]

Achim Blumensath, Felix Wolf
2019 arXiv   pre-print
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]

Uno Holmer, Kim Larsen, Wang Yi
1992 Lecture Notes in Computer Science  
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]

Patrick Blackburn, Johan van Benthem
2007 Studies in Logic and Practical Reasoning  
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

Martin Otto
2013 Annals of Pure and Applied Logic  
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]

Rogier M. van Eijk, Frank S. de Boer, Wiebe van der Hoek, John-Jules Ch. Meyer
2000 Lecture Notes in Computer Science  
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

Dilian Gurov, Marieke Huisman, Christoph Sprenger
2008 Information and Computation  
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]

Corina Cîrstea, Clemens Kupke, Dirk Pattinson
2009 Lecture Notes in Computer Science  
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]

Ranald Clouston, Rajeev Goré
2015 arXiv   pre-print
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]

Ranald Clouston, Rajeev Goré
2015 Lecture Notes in Computer Science  
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
« Previous Showing results 1 — 15 out of 673 results