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A Proof Theoretic Study of Soft Concurrent Constraint Programming

Published online by Cambridge University Press:  21 July 2014

ELAINE PIMENTEL ,
CARLOS OLARTE  and
VIVEK NIGAM
ELAINE PIMENTEL
Affiliation:
Universidade Federal do Rio Grande do Norte, Natal, Brazil (e-mail: elaine.pimentel@gmail.com)
CARLOS OLARTE
Affiliation:
Pontificia Universidad Javeriana Cali, Colombia, Universidade Federal do Rio Grande do Norte, Natal, Brazil (e-mail: carlos.olarte@gmail.com)
VIVEK NIGAM
Affiliation:
Universidade Federal da Paraíba, João Pessoa, Brazil (e-mail: vivek.nigam@gmail.com)
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Abstract

Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic. In fact, the underlying constraint system can be built from a suitable fragment of intuitionistic (linear) logic -ILL- and processes can be interpreted as formulas in ILL. Constraints as ILL formulas fail to represent accurately situations where “preferences” (called soft constraints) such as probabilities, uncertainty or fuzziness are present. In order to circumvent this problem, c-semirings have been proposed as algebraic structures for defining constraint systems where agents are allowed to tell and ask soft constraints. Nevertheless, in this case, the tight connection to logic and proof theory is lost. In this work, we give a proof theoretical meaning to soft constraints: they can be defined as formulas in a suitable fragment of ILL with subexponentials (SELL) where subexponentials, ordered in a c-semiring structure, are interpreted as preferences. We hence achieve two goals: (1) obtain a CCP language where agents can tell and ask soft constraints and (2) prove that the language in (1) has a strong connection with logic. Hence we keep a declarative reading of processes as formulas while providing a logical framework for soft-CCP based systems. An interesting side effect of (1) is that one is also able to handle probabilities (and other modalities) in SELL, by restricting the use of the promotion rule for non-idempotent c-semirings.This finer way of controlling subexponentials allows for considering more interesting spaces and restrictions, and it opens the possibility of specifying more challenging computational systems.

Keywords

Concurrent Constraint ProgrammingLinear LogicSoft Constraints
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Special Issue 4-5: 30th International Conference on Logic Programming , July 2014 , pp. 649 - 663
Copyright
Copyright © Cambridge University Press 2014 

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