101. A Proof Theoretic Study of Soft Concurrent Constraint Programming
- Author
-
Carlos Olarte, Elaine Pimentel, Vivek Nigam, Universidade Federal de Minas, Departamento de Matemática, Departamento de Electrónica, Pontificia Universidad Javeriana, and Pontificia Universidad Javeriana (PUJ)
- Subjects
FOS: Computer and information sciences ,Computer Science - Logic in Computer Science ,Theoretical computer science ,Computer science ,Concurrency ,concurrent constraint programming ,Theoretical Computer Science ,Soft Constraints ,Fragment (logic) ,Artificial Intelligence ,linear logic ,Constraint programming ,F.3.1 ,D.3.2 ,Structure (mathematical logic) ,ACM: D.: Software/D.3: PROGRAMMING LANGUAGES/D.3.2: Language Classifications/D.3.2.1: Concurrent, distributed, and parallel languages ,[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO] ,16. Peace & justice ,ACM: F.: Theory of Computation/F.3: LOGICS AND MEANINGS OF PROGRAMS/F.3.1: Specifying and Verifying and Reasoning about Programs ,Linear Logic ,Linear logic ,Logic in Computer Science (cs.LO) ,Constraint (information theory) ,Logical framework ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Computational Theory and Mathematics ,Hardware and Architecture ,Proof theory ,Concurrent Constraint Programming ,Software - 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.
- Published
- 2014