Probabilistic DL Reasoning with Pinpointing Formulas: A Prolog-based Approach

Abstract

When modeling real-world domains, we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we introduced a probabilistic semantics, named DISPONTE, in order to combine description logics (DLs) with probability theory. The probability of a query can be then computed from the set of its explanations by building a Binary Decision Diagram (BDD). The set of explanations can be found using thetableau algorithm, which has to handle non-determinism. Prolog, with its efficient handling of non-determinism, is suitable for implementing the tableau algorithm. TRILL and TRILLPare systems offering a Prolog implementation of the tableau algorithm. TRILLPbuilds apinpointing formulathat compactly represents the set of explanations and can be directly translated into a BDD. Both reasoners were shown to outperform state-of-the-art DL reasoners. In this paper, we present an improvement of TRILLP, named TORNADO, in which the BDD is directly built during the construction of the tableau, further speeding up the overall inference process. An experimental comparison shows the effectiveness of TORNADO. All systems can be tried online in the TRILL on SWISH web application athttp://trill.ml.unife.it/.

An Iterative Fixpoint Semantics for MKNF Hybrid Knowledge Bases with Function Symbols

“…We are currently working on a probabilistic extension of HKBs with function symbols, inspired by Sato's distribution semantics [14], which will be based on the iterated fixpoint operator defined in this paper. The probabilistic language of probabilistic HKB FS will be also equipped with a query answering system, in the style of what we did in TRILL [17,16] and PITA [13], comparing our system with that of Knorr and colleagues [9].…”

Optimizing a tableau reasoner and its implementation in Prolog

“…Probabilistic systems that can perform inference under DISPONTE are BUNDLE [12,13] and the TRILL framework. The first one is implemented in Java and it can exploit several non-probabilistic reasoners, the latter is a framework, written in Prolog, which contains three reasoners, namely, (i) TRILL [14,10], able to collect the set of all justifications and compute the probability of queries, (ii) TRILL [14,10], which implements in Prolog the tableau algorithm defined by Baader and Peñaloza [15,16] for returning the pinpoint-ing formula instead of the set of justifications, and (iii) TOR-NADO [17], which is similar to TRILL but represents the pinpointing formula in a way that can be directly used to compute the probability of the query.…”

“…The reasoners contained in the TRILL framework exploit Prolog's backtracking facilities for performing the search. In addition, the experiments performed by [17] showed that a Prolog implementation of the tableau algorithm can achieve competitive or even better results than other state-of-the-art (non-)probabilistic reasoners.…”

A Framework for Reasoning on Probabilistic Description Logics

“…Among them, in [27,36] we introduced the DISPONTE semantics, which applies the distribution semantics [30] to DLs. Examples of systems that perform probabilistic logic inference under DISPONTE are BUNDLE [27,28,36], and TRILL [38,36,37]. The former is implemented in Java, the latter in Prolog.…”

“…In this chapter, we illustrate the state of the art of the BUNDLE framework. In particular, we present a newer version of BUNDLE which also interfaces with the probabilistic reasoners of the TRILL system, namely: (i) TRILL [38,36], which solves the justification finding problem, (ii) TRILL P [38,36], which returns the pinpointing formula using the approach defined in [2,3], and (iii) TOR-NADO [37], which, similarly to TRILL P , returns the pinpointing formula, but the formula is represented in a way that can be directly used to compute the probability. In this way, the user can run probabilistic queries in a uniform way by using the preferred reasoner.…”