Toward an Infinitary Logic of Domains: Abramsky Logic for Transition Systems

@article{Bonsangue1999TowardAI,
  title={Toward an Infinitary Logic of Domains: Abramsky Logic for Transition Systems},
  author={Marcello M. Bonsangue and Joost N. Kok},
  journal={Inf. Comput.},
  year={1999},
  volume={155},
  pages={170-201}
}
We give a new characterization of sober spaces in terms of their completely distributive lattice of saturated sets. This characterization is used to extend Abramsky's results about a domain logic for transition systems. 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 prove that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual… 
Duality for Logics of Transition Systems
TLDR
A general framework for logics of transition systems based on Stone duality is presented to Vietoris coalgebras on topological spaces, using the duality between spaces and observation frames, to obtain adequate logics for transition systems on posets, sets, spectral spaces and Stone spaces.
Continuous L-domains in logical form
Presenting Functors by Operations and Equations
TLDR
A result is obtained that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.
The categorical equivalence between disjunctive sequent calculi and algebraic L-domains
This paper establishes a purely syntactic representation for the category of algebraic L-domains with Scott-continuous functions as morphisms. The central tool used here is the notion of logical
Infinite intersection types
A logic for Lawson compact algebraic L-domains
The Syntax of Disjunctive Propositional Logic and Algebraic L-domains
TLDR
A category of certain proof systems with consequence relations is shown to be equivalent to that of algebraic L-domains with Scott-continuous functions and a subclass of disjunctive propositional logic is found to provide a logical representation for Scott domains.
Infinite Intersection and Union Types for the Lazy Lambda Calculus
A type theory with infinitary intersection and union types for the lazy ?-calculus is introduced. Types are viewed as upper closed subsets of a Scott domain. Intersection and union type constructors
Domain µ-calculus
  • Guo-Qiang Zhang
  • Mathematics, Computer Science
    RAIRO Theor. Informatics Appl.
  • 2003
TLDR
This paper provides an improved formulation of a fragment of the μ-Calculus without function space or powerdomain constructions, and studies some open problems related to this μ-calculus such as decidability and expressive power.
Theoretical Informatics and Applications Domain Mu-calculus
TLDR
This paper provides an improved formulation of a fragment of the μ-Calculus without function space or powerdomain constructions, and studies some open problems related to this μ-calculus such as decidability and expressive power.
...
...

References

SHOWING 1-10 OF 54 REFERENCES
Infinitary Domain Logic for Finitary Transition Systems
TLDR
It is extended 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.
A Domain Equation for Bisimulation
TLDR
A denotational semantics for SCCS based on the domain of synchronization trees is given, and proved fully abstract with respect to bisimulation.
Domain Theory in Logical Form
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
A program logic for gamma
TLDR
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.
Concurrency and Automata on Infinite Sequences
  • D. Park
  • Computer Science
    Theoretical Computer Science
  • 1981
TLDR
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.
Domain theory
bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the
Free Completely Distributive Lattices
We show that the usual construction of the free distributive lattice on n generators generalizes to an arbitrary quantity of generators and actually yields a free completely distributive lattice.
Algebraic laws for nondeterminism and concurrency
TLDR
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.
...
...