A Stochastic Pi Calculus for Concurrent Objects

International audienceWe present SpiCO, a new modeling and simulation language for system biology, based on the stochastic pi-calculus. SpiCO supports higher level modeling via multi-profile concurrent objects with static inheritance. We present a semantics for SpiCO in terms of continuous time Markov chains, and show how to compile SpiCO back into the biochemical stochastic pi-calculus while preserving semantics

Psi-calculi: a framework for mobile processes with nominal data and logic

The framework of psi-calculi extends the pi-calculus with nominal datatypes for data structures and for logical assertions and conditions. These can be transmitted between processes and their names can be statically scoped as in the standard pi-calculus. Psi-calculi can capture the same phenomena as other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, the concurrent constraint pi-calculus, and calculi with polyadic communication channels or pattern matching. Psi-calculi can be even more general, for example by allowing structured channels, higher-order formalisms such as the lambda calculus for data structures, and predicate logic for assertions. We provide ample comparisons to related calculi and discuss a few significant applications. Our labelled operational semantics and definition of bisimulation is straightforward, without a structural congruence. We establish minimal requirements on the nominal data and logic in order to prove general algebraic properties of psi-calculi, all of which have been checked in the interactive theorem prover Isabelle. Expressiveness of psi-calculi significantly exceeds that of other formalisms, while the purity of the semantics is on par with the original pi-calculus.Comment: 44 page

A randomized encoding of the pi-calculus with mixed choice

International audienceWe consider the problem of encoding the pi-calculus with mixed choice into the asynchronous pi-calculus via a uniform translation while preserving a reasonable semantics. Although it has been shown that this is not possible with an exact encoding, we suggest a randomized approach using a probabilistic extension of the asynchronous pi-calculus, and we show that our solution is correct with probability 1 under any proper adversary wrt a notion of testing semantics. This result establishes the basis for a distributed and symmetric implementation of mixed choice which, differently from previous proposals in literature, does not rely on assumptions on the relative speed of processes and it is robust to attacks of proper adversaries

A Stochastic Pi Calculus for Concurrent Objects

International audienceWe present SpiCO, a new modeling and simulation language for system biology, based on the stochastic pi-calculus. SpiCO supports higher level modeling via multi-profile concurrent objects with static inheritance. We present a semantics for SpiCO in terms of continuous time Markov chains, and show how to compile SpiCO back into the biochemical stochastic pi-calculus while preserving semantics

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica

Proof Search Specifications of the pi-calculus

International audienceWe specify the operational semantics and bisimulation relations for the finite pi-calculus within a logic that contains the nabla quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The nabla quantifier helps with the delicate issues surrounding the scope of variables within pi-calculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no side-conditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (forall, exists, and nabla) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for one-step transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the pi-calculus with replications, in an extended logic with induction and co-induction

A Fully Abstract Symbolic Semantics for Psi-Calculi

We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Psi-calculi can be more general than other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, or the concurrent constraint pi-calculus. Symbolic semantics are necessary for an efficient implementation of the calculus in automated tools exploring state spaces, and the full abstraction property means the semantics of a process does not change from the original

Primitives for Contract-based Synchronization

We investigate how contracts can be used to regulate the interaction between processes. To do that, we study a variant of the concurrent constraints calculus presented in [1], featuring primitives for multi-party synchronization via contracts. We proceed in two directions. First, we exploit our primitives to model some contract-based interactions. Then, we discuss how several models for concurrency can be expressed through our primitives. In particular, we encode the pi-calculus and graph rewriting.Comment: In Proceedings ICE 2010, arXiv:1010.530