A Simple Complete Search for Logic Programming

Here, we present a family of complete interleaving depth-first search strategies for embedded, domain-specific logic languages. We derive our search family from a stream-based implementation of incomplete depth-first search. The DSL\u27s programs\u27 texts induce particular strategies guaranteed to be complete

Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

Inductive Logic Programming considers almost exclusively universally quantied theories. To add expressiveness, prenex conjunctive normal forms (PCNF) with existential variables should also be considered. ILP mostly uses learning with refinement operators. To extend refinement operators to PCNF, we should first do so with substitutions. However, applying a classic substitution to a PCNF with existential variables, one often obtains a generalization rather than a specialization. In this article we define substitutions that specialize a given PCNF and a weakly complete downward refinement operator. Moreover, we analyze the complexities of this operator in different types of languages and search spaces. In this way we lay a foundation for learning systems on PCNF. Based on this operator, we have implemented a simple learning system PCL on some type of PCNF.learning;PCNF;completeness;refinement;substitutions

Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

Inductive Logic Programming considers almost exclusively universally quantied theories. To add expressiveness, prenex conjunctive normal forms (PCNF) with existential variables should also be considered. ILP mostly uses learning with refinement operators. To extend refinement operators to PCNF, we should first do so with substitutions. However, applying a classic substitution to a PCNF with existential variables, one often obtains a generalization rather than a specialization. In this article we define substitutions that specialize a given PCNF and a weakly complete downward refinement operator. Moreover, we analyze the complexities of this operator in different types of languages and search spaces. In this way we lay a foundation for learning systems on PCNF. Based on this operator, we have implemented a simple learning system PCL on some type of PCNF

Experiments in reactive constraint logic programming1This paper is the complete version of a previous paper published in [14].1

AbstractIn this paper we study a reactive extension of constraint logic programming (CLP). Our primary concerns are search problems in a dynamic environment, where interactions with the user (e.g. in interactive multi-criteria optimization problems) or interactions with the physical world (e.g. in time evolving problems) can be modeled and solved efficiently. Our approach is based on a complete set of query manipulation commands for both the addition and the deletion of constraints and atoms in the query. We define a fully incremental model of execution which, contrary to other proposals, retains as much information as possible from the last derivation preceding a query manipulation command. The completeness of the execution model is proved in a simple framework of transformations for CSLD derivations, and of constraint propagation seen as chaotic iteration of closure operators. A prototype implementation of this execution model is described and evaluated on two applications

ON SIMPLE BUT HARD RANDOM INSTANCES OF PROPOSITIONAL THEORIES AND LOGIC PROGRAMS

In the last decade, Answer Set Programming (ASP) and Satisfiability (SAT) have been used to solve combinatorial search problems and practical applications in which they arise. In each of these formalisms, a tool called a solver is used to solve problems. A solver takes as input a specification of the problem – a logic program in the case of ASP, and a CNF theory for SAT – and produces as output a solution to the problem. Designing fast solvers is important for the success of this general-purpose approach to solving search problems. Classes of instances that pose challenges to solvers can help in this task. In this dissertation we create challenging yet simple benchmarks for existing solvers in ASP and SAT.We do so by providing models of simple logic programs as well as models of simple CNF theories. We then randomly generate logic programs as well as CNF theories from these models. Our experimental results show that computing answer sets of random logic programs as well as models of random CNF theories with carefully chosen parameters is hard for existing solvers. We generate random logic programs with 2-literals, and our experiments show that it is hard for ASP solvers to obtain answer sets of purely negative and constraint-free programs, indicating the importance of these programs in the development of ASP solvers. An easy-hard-easy pattern emerges as we compute the average number of choice points generated by ASP solvers on randomly generated 2-literal programs with an increasing number of rules. We provide an explanation for the emergence of this pattern in these programs. We also theoretically study the probability of existence of an answer set for sparse and dense 2-literal programs. We consider simple classes of mixed Horn formulas with purely positive 2- literal clauses and purely negated Horn clauses. First we consider a class of mixed Horn formulas wherein each formula has m 2-literal clauses and k-literal negated Horn clauses. We show that formulas that are generated from the phase transition region of this class are hard for complete SAT solvers. The second class of Mixed Horn Formulas we consider are obtained from completion of a certain class of random logic programs. We show the appearance of an easy-hard-easy pattern as we generate formulas from this class with increasing numbers of clauses, and that the formulas generated in the hard region can be used as benchmarks for testing incomplete SAT solvers

Logic programming in the context of multiparadigm programming: the Oz experience

Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential, concurrent, etc.) with equal ease. This article has two goals: to give a tutorial of logic programming in Oz and to show how logic programming fits naturally into the wider context of multiparadigm programming. Our experience shows that there are two classes of problems, which we call algorithmic and search problems, for which logic programming can help formulate practical solutions. Algorithmic problems have known efficient algorithms. Search problems do not have known efficient algorithms but can be solved with search. The Oz support for logic programming targets these two problem classes specifically, using the concepts needed for each. This is in contrast to the Prolog approach, which targets both classes with one set of concepts, which results in less than optimal support for each class. To explain the essential difference between algorithmic and search programs, we define the Oz execution model. This model subsumes both concurrent logic programming (committed-choice-style) and search-based logic programming (Prolog-style). Instead of Horn clause syntax, Oz has a simple, fully compositional, higher-order syntax that accommodates the abilities of the language. We conclude with lessons learned from this work, a brief history of Oz, and many entry points into the Oz literature.Comment: 48 pages, to appear in the journal "Theory and Practice of Logic Programming

Probabilistic Constraint Logic Programming

This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for probabilistic regular and context-free models. We address these problems for a more expressive probabilistic constraint logic programming model. We present a log-linear probability model for probabilistic constraint logic programming. On top of this model we define an algorithm to estimate the parameters and to select the properties of log-linear models from incomplete data. This algorithm is an extension of the improved iterative scaling algorithm of Della-Pietra, Della-Pietra, and Lafferty (1995). Our algorithm applies to log-linear models in general and is accompanied with suitable approximation methods when applied to large data spaces. Furthermore, we present an approach for searching for most probable analyses of the probabilistic constraint logic programming model. This method can be applied to the ambiguity resolution problem in natural language processing applications.Comment: 35 pages, uses sfbart.cl