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From Logic to Stochastic Processes

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Prakash Panangaden

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To appear at the 2nd International Conference on Principles and Practice of
Declarative Programming (PPDP 2000), Montreal, Canada, September 20-22, 2000

### Abstract

The evolution of the concurrent constraint programming paradigm is a striking
illustration of the evolution of computer science. Fifteen years ago
probability was a special topic of interest to complexity and algorithm
peoples and hybrid systems were new and exotic. Now there are conferences
and workshops devoted to probabilistic systems, hybrid systems and verification.
The concurrent constraint paradigm has similarly assimilated ideas from
AI, probability and even analysis and become far richer for it.
I will give a survey of developments in the cc languages from plain cc to --
the as yet undiscovered -- stochastic cc. Roughly speaking, one can trace
the development as follows. The original cc languages were developed as a
concurrent programming language with the constraint system as a parameter.
They abstracted from the variety of control mechanisms that were current
then in concurrent logic programming languages and in functional languages
with so called "logic variables". The cc family was purely asynchronous.

In order to express reactive programs as in the family of synchronous
languages one had to introduce time. This led to the language tcc which
captured temporal notions. However, for synchronous programs one needs
an orthogonal idea as well, that of a default.

The presence of defaults introduces nonmonotonicity into the language.
As we refine the notion of time and introduce a mixture of continuous
time as well as discrete time we get a hybrid language called hcc. In fact
the language of this name developed by Gupta, Jagadeesan and Saraswat has
hybrid time-evolution and defaults, we will call it hdcc.

In 1997 Gupta, Jagadeesan and Saraswat introduced a probabilistic cc language
and in 1999 this was extended to handle recursion by Gupta, Jagadeesan and
Panangaden. In later investigation we noticed that one could use probabilities
instead of defaults. In other words the way probability works one can
emulate the effect of defaults. Thus if one were to add time to Probcc
one would have the effect of the language tdcc or -- if one adds continuous
time -- hdcc. We are currently working on the development of a modelling
language analogous to hdcc for dealing with general stochastic differential
equations in the same way hdcc deals with differential equations.