Disjunctive Answer Set Solvers via Templates

Answer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set solvers are the programs that perform this task. The problem of deciding whether a disjunctive program has a stable model is $\Sigma^P_2$-complete. The high complexity of reasoning within disjunctive logic programming is responsible for few solvers capable of dealing with such programs, namely DLV, GnT, Cmodels, CLASP and WASP. In this paper we show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for disjunctive answer set solvers. Transition systems give a unifying perspective and bring clarity in the description and comparison of solvers. They can be effectively used for analyzing, comparing and proving correctness of search algorithms as well as inspiring new ideas in the design of disjunctive answer set solvers. In this light, we introduce a general template, which accounts for major techniques implemented in disjunctive solvers. We then illustrate how this general template captures solvers DLV, GnT and Cmodels. We also show how this framework provides a convenient tool for designing new solving algorithms by means of combinations of techniques employed in different solvers.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Resource Usage Analysis from a Different Perspective on MOOC Dropout

We present a novel learning analytics approach, for analyzing the usage of resources in MOOCs. Our target stakeholders are the course designers who aim to evaluate their learning materials. In order to gain insight into the way educational resources are used, we view dropout behaviour in an atypical manner: Instead of using it as an indicator of failure, we use it as a mean to compute other features. For this purpose, we developed a prototype, called RUAF, that can be applied to the data format provided by FutureLearn. As a proof of concept, we perform a study by applying this tool to the interaction data of learners from four MOOCs. We also study the quality of our computations, by comparing them to existing process mining approaches. We present results that highlight patterns showing how learners use resources. We also show examples of practical conclusions a course designer may benefit from.Comment: 30 pages, 40 figure

Technical Communications of ICLP

Abstract Abstract solvers are a recently employed method to formally analyze algorithms that earns some advantages w.r.t. traditional ways such as pseudo-code-based description. Abstract solvers proved to be a useful tool for describing, comparing and composing solving techniques in various fields such as SAT, SMT, ASP, CASP. In ASP, abstract solvers have been so far employed for describing solvers for brave reasoning tasks. In this paper we apply, for the first time, this methodology to the analysis of ASP solvers for cautious reasoning tasks. We describe and compare the available approaches in the literature, which employ techniques for computing over-and under-approximations of the solution, the last including "coherence tests" for deciding the inclusion of a single atom in the solution, a technique borrowed from backbone computation of CNF formulas. Then, we show how to improve the current abstract solvers with new techniques, in order to design new solving algorithms

On the almighty wand

We investigate decidability, complexity and expressive power issues for (first-order) separation logic with one record field (herein called SL) and its fragments. SL can specify properties about the memory heap of programs with singly-linked lists. Separation logic with two record fields is known to be undecidable by reduction of finite satisfiability for classical predicate logic with one binary relation. Surprisingly, we show that second-order logic is as expressive as SL and as a by-product we get undecidability of St.. This is refined by showing that SL without the separating conjunction is as expressive as SL, whence undecidable too. As a consequence, in SL the separating implication (also known as the magic wand) can simulate the separating conjunction. By contrast, we establish that SL without the magic wand is decidable, and we prove a non-elementary complexity by reduction from satisfiability for the first-order theory over finite words. This result is extended with a bounded use of the magic wand that appears in Hoare-style rules. As a generalization, it is shown that kSL, the separation logic over heaps with k >= 1 record fields, is equivalent to kSO, the second-order logic over heaps with k record fields. (C) 2012 Elsevier Inc. All rights reserved