Efficient Maximum A-Posteriori Inference in Markov Logic and Application in Description Logics

Maximum a-posteriori (MAP) query in statistical relational models computes the most probable world given evidence and further knowledge about the domain. It is arguably one of the most important types of computational problems, since it is also used as a subroutine in weight learning algorithms. In this thesis, we discuss an improved inference algorithm and an application for MAP queries. We focus on Markov logic (ML) as statistical relational formalism. Markov logic combines Markov networks with first-order logic by attaching weights to first-order formulas. For inference, we improve existing work which translates MAP queries to integer linear programs (ILP). The motivation is that existing ILP solvers are very stable and fast and are able to precisely estimate the quality of an intermediate solution. In our work, we focus on improving the translation process such that we result in ILPs having fewer variables and fewer constraints. Our main contribution is the Cutting Plane Aggregation (CPA) approach which leverages symmetries in ML networks and parallelizes MAP inference. Additionally, we integrate the cutting plane inference (Riedel 2008) algorithm which significantly reduces the number of groundings by solving multiple smaller ILPs instead of one large ILP. We present the new Markov logic engine RockIt which outperforms state-of-the-art engines in standard Markov logic benchmarks. Afterwards, we apply the MAP query to description logics. Description logics (DL) are knowledge representation formalisms whose expressivity is higher than propositional logic but lower than first-order logic. The most popular DLs have been standardized in the ontology language OWL and are an elementary component in the Semantic Web. We combine Markov logic, which essentially follows the semantic of a log-linear model, with description logics to log-linear description logics. In log-linear description logic weights can be attached to any description logic axiom. Furthermore, we introduce a new query type which computes the most-probable 'coherent' world. Possible applications of log-linear description logics are mainly located in the area of ontology learning and data integration. With our novel log-linear description logic reasoner ELog, we experimentally show that more expressivity increases quality and that the solutions of optimal solving strategies have higher quality than the solutions of approximate solving strategies

Detailed and GlobalAnalysis of a Remedial Course's Impact on Incoming Students' Marks

Engineering incoming students are facing great difficulties to overcome first course subjects. To tackle that situation and increase the students’ success a Remedial course in Mathematics was offered to Informatics Engineering freshmen. This study presents a statistical analysis of their results comparing the marks obtained by those joining the course (studio group) versus those who did not participate (control group). ANOVA tests are performed over the students’ marks averages as well as over each subject students marks. These tests show statistically significant differences between both groups, with the studio group consistently outperforming the control group at 99% confidence level in most cases and at more than 92% confidence level in every case

Named Models in Coalgebraic Hybrid Logic

Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding

Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions