Design and Implementation of a Concurrent Logic Programming Language with Linear Logic Constraints

My thesis aims at designing a practical language as close as possible to the linear concurrent constraint (LCC) theory. The main contribution is a new operational semantics which behaves as an angelic scheduler with a tractable algorithmic complexity. This operational semantics is sound and complete with respect to the logical semantics and allows the construction of a rich language over a very simple kernel

CHR(PRISM)-based Probabilistic Logic Learning

PRISM is an extension of Prolog with probabilistic predicates and built-in support for expectation-maximization learning. Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. In this paper, we introduce a new probabilistic logic formalism, called CHRiSM, based on a combination of CHR and PRISM. It can be used for high-level rapid prototyping of complex statistical models by means of "chance rules". The underlying PRISM system can then be used for several probabilistic inference tasks, including probability computation and parameter learning. We define the CHRiSM language in terms of syntax and operational semantics, and illustrate it with examples. We define the notion of ambiguous programs and define a distribution semantics for unambiguous programs. Next, we describe an implementation of CHRiSM, based on CHR(PRISM). We discuss the relation between CHRiSM and other probabilistic logic programming languages, in particular PCHR. Finally we identify potential application domains

(Co-)Inductive semantics for Constraint Handling Rules

In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over the transition system generated by the abstract operational semantics of CHR. Similarly, we demonstrate that the logical reading of states with respect to a set of propagation rules can be characterized by a greatest fixpoint. Then, in order to take advantage of both types of rules without losing fixpoint characterization, we present an operational semantics with persistent. We finally establish that this semantics can be characterized by two nested fixpoints, and we show the resulting language is an elegant framework to program using coinductive reasoning.Comment: 17 page

Constraint Handling Rules with Binders, Patterns and Generic Quantification

Constraint Handling Rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the term syntax of constraints is replaced by $\lambda$-tree syntax, in which binding is explicit; and a new $\nabla$ generic quantifier is introduced, which is used to create new fresh constants.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no PDF figure

A Linear Logic Programming Language for Concurrent Programming over Graph Structures

We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be consumed. Because LM integrates both classical and linear logic, LM tends to be more expressive than other logic programming languages. LM programs are naturally concurrent because facts are partitioned by nodes of a graph data structure. Computation is performed at the node level while communication happens between connected nodes. In this paper, we present the syntax and operational semantics of our language and illustrate its use through a number of examples.Comment: ICLP 2014, TPLP 201

Logical Algorithms meets CHR: A meta-complexity result for Constraint Handling Rules with rule priorities

This paper investigates the relationship between the Logical Algorithms language (LA) of Ganzinger and McAllester and Constraint Handling Rules (CHR). We present a translation schema from LA to CHR-rp: CHR with rule priorities, and show that the meta-complexity theorem for LA can be applied to a subset of CHR-rp via inverse translation. Inspired by the high-level implementation proposal for Logical Algorithm by Ganzinger and McAllester and based on a new scheduling algorithm, we propose an alternative implementation for CHR-rp that gives strong complexity guarantees and results in a new and accurate meta-complexity theorem for CHR-rp. It is furthermore shown that the translation from Logical Algorithms to CHR-rp combined with the new CHR-rp implementation, satisfies the required complexity for the Logical Algorithms meta-complexity result to hold.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Implementing probabilistic abductive logic programming with Constraint Handling Rules

Abstract. A class of Probabilistic Abductive Logic Programs (PALPs) is introduced and an implementation is developed in CHR for solving abductive problems, providing minimal explanations with their probabilities. Both all-explanations and most-probable-explanations versions are given. Compared with other probabilistic versions of abductive logic programming, the approach is characterized by higher generality and a flexible and adaptable architecture which incorporates integrity constraints and interaction with external constraint solvers. A PALP is transformed in a systematic way into a CHR program which serves as a query interpreter, and the resulting CHR code describes in a highly concise way, the strategies applied in the search for explanations

User-definable rule priorities for CHR

This paper introduces CHR-rp: Constraint Handling Rules with user-definable rule priorities. CHR-rp offers flexible execution control which is lacking in CHR. A formal operational semantics for the extended language is given and is shown to be an instance of the theoretical operational semantics of CHR. It is discussed how the CHR-rp semantics influences confluence results. A translation scheme for CHR-rp programs with static rule priorities into (regular) CHR is presented. The translation is proven correct and benchmark results are given. CHR-rp is related to priority systems in other constraint programming and rule based languages.status: publishe