Infinitary Domain Logic for Finitary Transition Systems

  title={Infinitary Domain Logic for Finitary Transition Systems},
  author={Marcello M. Bonsangue and Joost N. Kok},
The Lindenbaum algebra generated by the Abramsky finitary logic is a distributive lattice dual to an SFP-domain obtained as a solution of a recursive domain equation. We extend Abramsky's result by proving that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain. As a consequence soundness and completeness of the infinitary logic is obtained for the class of finitary transition systems. A corollary of this result is that the… 
Toward an Infinitary Logic of Domains: Abramsky Logic for Transition Systems
It is proved that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain.


Concurrency and Automata on Infinite Sequences
  • D. Park
  • Computer Science
    Theoretical Computer Science
  • 1981
A general method for proving/deciding equivalences between omega-regular languages, whose recognizers are modified forms of Buchi or Muller-McNaughton automata, derived from Milner's notion of “simulation” is obtained.
Re-interpreting the Modal -calculus
We reexamine the modal-calculus in the light of some classical theory of Boolean algebras and recent results on duality theory for a modal logic with xed points. We propose interpreting formulas into
Domain Theory in Logical Form
A program logic for gamma
This work starts from a resumption semantics of Gamma, and is able to derive both the formulae and the proof system of the transition assertion logic previously proposed by Errington, Hankin and Jensen.
Algebraic laws for nondeterminism and concurrency
The paper demonstrates, for a sequence of simple languages expressing finite behaviors, that in each case observation congruence can be axiomatized algebraically and the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.
Power Domains and Predicate Transformers: A Topological View
The specific tasks are to provide a more adequate framework for power-domain constructions; and to show that the connection between (Dijkstra's) weakest preconditions and the Smyth powerdomain, established by Plotkin for the case of flat domains, actually holds in full generality.
Topology via Logic
1. Introduction 2. Affirmative and refutative assertions 3. Frames 4. Frames as algebras 5. Topology: the definitions 6. New topologies for old 7. Point logic 8. Compactness 9. Spectral algebraic
A Calculus of Communicating Systems
  • R. Milner
  • Computer Science
    Lecture Notes in Computer Science
  • 1980
A case study in synchronization and proof techniques, and some proofs about data structures in value-communication as a model of CCS 2.0.
Logic of Domains
I SFP Domains.- 1 Introduction.- 2 Prerequisites.- 3 A Representation of SFP.- 4 A Logic of SFP.- 5 A Mu-Calculus.- II Stable Domains.- 6 Categories.- 7 A Representation of DI.- 8 Stable