A Spatial Concurrent-Constraint Calculus _First Report_

Document Sample

```					                   Introduction
Concurrent Constraint System
A Simple Example

A Spatial Concurrent-Constraint Calculus
(First Report)

John Alexander Vargas

Forces, 2009

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction
Concurrent Constraint System
A Simple Example

Preliminars

The Concurrent Constraint Programing is a formalism for
reasoning about agents which interact with each other by
telling and asking information represented as logic formulas
The agent can viewed as both process and formulas in the
underlying logic.
The Ambient Calculus model de behavior and structure of
mobile systems.
The Spatial Logic can be use to specify properties of these
systems.
The utcc calculus allow for the specication of mobile
behaviors in the sense of π -calculus

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction
Concurrent Constraint System
A Simple Example

Research Proposal

The BioAmbients Calculus is an abstraction for biomolecular
systems using the π -calculus for modeling molecular and
biochemical aspects and ambients calculus for specication of
process location and movement.
Mi research proposal is explore the use utcc with spatial logic
as underlyng logic of constraint system for modeling mobile
properties.
Model and study a complex multi-cellular system: The
hypothalamic weight regulation system

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction
Concurrent Constraint System
A Simple Example

Metodology

The metodology is:
1   To dene formaly a constraint system with spatial logic as
underlyng logic.
2   To model a simple example with utcc and spatial constraint
system.
3   Verify spatial properties that satisfy with this calculus.
4   To model the hypothalamic weight regulation system with this
calculus.
5   Verify that mobile properties can be modeled with this
calculus.

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction
Concurrent Constraint System
A Simple Example

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Logical Formulas and Satisfaction

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Example

P       a[m[out a. in b. < c >]] | b[open m. (n). n[]]

P |= a[T] | b[T] | T        P includes locations a and b
P |= a[m[T]] | T            there is a location m in a
P |= ♦(b[m[T] | T])         a location m will be found in b
P |= ♦ c []                 an empty location c will be produced

(a[m[T]]|T) ∧ ♦(b[m[T] | T])

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Quantiers

Fresh-Name Quantier
P |= x .A       ∃m ∈ Λ, m ∈ fn(P , A) ∧ P |= A{x ← m}
/
P |= x .A       ∀m ∈ Λ, m ∈ fn(P , A) ∧ P |= A{x ← m}
/
because any fresh name is as good as any other.

Hidden-Name Quantier
P |=Hx .Ai ∃m ∈ Λ, P ∈ Π m ∈ fn(A) ∧ P ≡ (v m)P ∧ P |=
/     /
A{x ← m}

Hx .A         x .x R A

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Describing spatial properties of concurrent systems
This Spatial Logics are used to specify the behavior and spatial
structure of concurrent systems, properties as a fresh or secret
resources such as keys, nonces, channels, and locations.

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Propositional

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Composition

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Locations

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Modalities

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Revelation

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Example of Deduction

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Spatial Logic for nite trees

Due to the growing popularity of semistructured data, and
particularly XML, there is a renewed interest in typed
programming languages that can manipulate tree-like data
structures.
Spatial Logics was proposed as a rich description language for
tree-like data.
View the spatial logics as a type system to semi-structured
data.

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Sequent Calculus

In [CalCarGor02] presented a sequent calculus for spatial logics
of ambients. And show that this calculus is sound and
complete with respect to an interpretation in terms of the
satisfaction relation, and present a complete proof procedure.
A context, Γ or ∆, is a nite multiset of entries of the form
P : A where P is a tree and A is a formula. A sequent is a
judgment Γ ∆ ` where Γ and ∆ are contexts.

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Rules of the sequents calculus

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Rules of Sequent Calculus

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Spatial Logic
Concurrent Constraint System   Logical Inference Rules
A Simple Example    Deciding Validity by Deduction

Decidability

Theorem
(Complete Proof Procedure)
For any Γ ∆ there is a procedure such that: if ¬[[ Γ ∆ ]], then
the procedure terminates with failure; if [[ Γ ∆ ]], then the
procedure terminates with a derivation for Γ ∆ .

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Modeling Ambients in utcc with Spatial Logics

P a[inb.P ], Q b[0], then the reduction of P | Q
a[inb.R ] | b[0] → b[a[R ]]
P tell (a[R ]) || (abs T1 , T2 ; a[T1 ] | b[T2 ]) tell (b[a[T1 ] | T2 ])
Q tell (b[0])
P a[out b.R ], then the reduction of b[P ]
b[a[out b.R ]] → b[0] | a[R ]
P tell (a[R ]) || (abs T1 , T2 ; b[a[T1 ] | T2 ]) tell ( b[T2 ] | a[T1 ] )
Q tell (b[a[R ]])
P openb.R , Q b[S ], then the reduction of P | Q
openb.R | b[S ] → R | S
P tell ( R ) (abs T1 , T2 ; b[T1 ] | T2 ) tell (T1 | T2 )
Q tell (b[R ])

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Modeling Ambients in utcc with Spatial Logics

P a[inb.P ], Q b[0], then the reduction of P | Q
a[inb.R ] | b[0] → b[a[R ]]
P tell (a[R ]) || (abs T1 , T2 ; a[T1 ] | b[T2 ]) tell (b[a[T1 ] | T2 ])
Q tell (b[0])
P a[out b.R ], then the reduction of b[P ]
b[a[out b.R ]] → b[0] | a[R ]
P tell (a[R ]) || (abs T1 , T2 ; b[a[T1 ] | T2 ]) tell ( b[T2 ] | a[T1 ] )
Q tell (b[a[R ]])
P openb.R , Q b[S ], then the reduction of P | Q
openb.R | b[S ] → R | S
P tell ( R ) (abs T1 , T2 ; b[T1 ] | T2 ) tell (T1 | T2 )
Q tell (b[R ])

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Modeling Ambients in utcc with Spatial Logics

P a[inb.P ], Q b[0], then the reduction of P | Q
a[inb.R ] | b[0] → b[a[R ]]
P tell (a[R ]) || (abs T1 , T2 ; a[T1 ] | b[T2 ]) tell (b[a[T1 ] | T2 ])
Q tell (b[0])
P a[out b.R ], then the reduction of b[P ]
b[a[out b.R ]] → b[0] | a[R ]
P tell (a[R ]) || (abs T1 , T2 ; b[a[T1 ] | T2 ]) tell ( b[T2 ] | a[T1 ] )
Q tell (b[a[R ]])
P openb.R , Q b[S ], then the reduction of P | Q
openb.R | b[S ] → R | S
P tell ( R ) (abs T1 , T2 ; b[T1 ] | T2 ) tell (T1 | T2 )
Q tell (b[R ])

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Spatial Formulas in utcc

P tell (n[R ] m[S ])
Q (abs T1 ; m[T1 ]) tell R @n
P ||Q || tell n[R ]

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Example in Ambient Calculus

Firewall (vw )w [k [out w . in k . in w ] | open k . open k .P ]
Agent k [open k .k [Q ]]
(v k k k )(Agent | Firewall ) = (v w )w [Q | P ]
∼

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Example in tcc

Firewall                                       Agent
(local w )                                     tell ( k [k [Q ]] ) ||
tell (w [P ] | k [0]) ||                   (abs T1 , T2 ; k [k [T1 ]|T2 ])
(abs T1 , T2 ; k [T1 ]|k [T2 ] )                (tell ( k [T1 |T2 ] ) )
( tell ( k [k [T2 ]|T1 ] ) ||
(abs A, B ; w [A]|k [B ] )
(tell ( w [A|k [B ]] ))
) ||
(abs   T1 , T2 ; w [k [T1 ]|T2 ])
(tell (w [T1 |T2 ]) ||
(abs A, B ; w [k [A]|B ] )
( tell (w [A|B ]) )
)

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Outline

1   Introduction

2   Concurrent Constraint System
Spatial Logic
Logical Inference Rules
Deciding Validity by Deduction

3   A Simple Example
Modeling Ambients in utcc
Firewall and Agent
Rules of Satisfaction of utcc process

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction      Modeling Ambients in utcc
Concurrent Constraint System      Firewall and Agent
A Simple Example       Rules of Satisfaction of utcc process

Satisfaction

tell (c ) |= c
P |=A
(local x , c )P |=Hx .A

P |=A
(abs x , c )P |=Nx .c ∧Hx .A

P |=A∧Q |=B
P | Q |=A | B
P |=A
next P |=◦A

John Alexander Vargas       A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

Future Work

Study the model of hypothalamic weight regulation system in
bioambients.
Model this biological system with sccp
Study mobile properties in sccp.

John Alexander Vargas    A Spatial Concurrent-Constraint Calculus (First Report)
Introduction   Modeling Ambients in utcc
Concurrent Constraint System   Firewall and Agent
A Simple Example    Rules of Satisfaction of utcc process

References
Cristiano Calcagno Luca Cardelli Andrew D. Gordon Deciding
Validity in a Spatial Logic for Trees, 2002
Luca Cardelli, Adrew Gordon. Logical Properties of Name
Restriction.
Luca Cardelli y Andrew Gordón. Mobile Ambients. 1997.
Luca Cardelli y Andrew Gordon. Ambient Logic. 2003
Luis Caires y Luca Cardelli. A Spatial Logic for Concurrency
(Part I). 2007
Carlos Olarte, Catuscia Palamidesi y Frank Valencia. Universal
Timed Concurrent Constraint Programming. 2007
Aviv Regev, E. Panina, W Silverman, L Cardelli y E. Shapiro.
BioAmbients: An abstraction for biological compartments. 2003