Implementing an Efficient SAT Solver for a Probabilistic Description Logic

Mapping Intimacies ◽

10.29007/wm7w ◽

2018 ◽

Author(s):

Pavel Klinov ◽

Bijan Parsia

Keyword(s):

Column Generation ◽

Description Logic ◽

Empirical Investigation ◽

Knowledge Bases ◽

Probabilistic Logic ◽

Linear Programs ◽

Probabilistic Description ◽

Probabilistic Knowledge ◽

Sat Solver ◽

Straightforward Approach

This paper presents an optimized algorithm for solving the satisfiability problem (PSAT) in the probabilistic description logic P-SROIQ. P-SROIQ and related Nilsson-style probabilistic logics the PSAT problem is typically solved by reduction to linear programming. This straightforward approach does not scale well because the number of variables in linear programs grows exponentially with the number of probabilistic statements. In this paper we demonstrate an algorithm to cope with this problem which is based on column generation. Although column generation approaches to PSAT have been known for the last two decades, this is, to the best of our knowledge, the first algorithm which also works for a non-propositional probabilistic logic. We report results of an empirical investigation which show that the algorithm can handle probabilistic knowledge bases of about 1000 probabilistic statements in addition to even larger number of classical SROIQ axioms.

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Secrecy-Preserving Reasoning and Query Answering in Probabilistic Description Logic Knowledge Bases

10.29007/npd4 ◽

2018 ◽

Author(s):

Gopalakrishnan Krishnasamy Sivaprakasam ◽

Adrienne Raglin ◽

Douglas Summers-Stay ◽

Giora Slutzki

Keyword(s):

Probabilistic Model ◽

Description Logic ◽

Knowledge Bases ◽

Query Answering ◽

Decomposition Algorithm ◽

Probabilistic Description ◽

Recursive Query ◽

Finite Set ◽

The Given

In this paper we study Secrecy-Preserving Query Answering problem underthe OpenWorld Assumption (OWA) for Prob-EL>0;=1 Knowledge Bases(KBs). We have designed a tableau procedure to compute a semi model Mover the given KB which eventually is equivalent to a probabilistic modelto KB. Given a secrecy set S, which is a finite set of assertions, wecompute a function E, called an envelope of S, which assigns a set E() ofassertions to each world in the semi modal M. E provides logical protection to the secrecy set S against the reasoning of a querying agent. Once the semi model M and an envelope E are computed, we define the secrecy-preserving semi model ME.Based on the information available in ME, assertional queries with probabilisticoperators can be answered eciently while preserving secrecy. Tothe best of our knowledge, this work is first one studying secrecy-preservingreasoning in description logic augmented with probabilistic operators. Whenthe querying agent asks a query q, the reasoner answers “Yes” if informationabout q is available in ME; otherwise, the reasoner answers “Unknown”. Beingable to answer “Unknown” plays a key role in protecting secrecy underOWA. Since we are not computing all the consequences of the knowledgebase, answers to the queries based on just secrecy-preserving semi modelME could be erroneous. To fix this problem, we further augment our algorithmsby providing recursive query decomposition algorithm to make thequery answering procedure foolproof.1

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Measuring Inconsistency in Probabilistic Knowledge Bases

10.5753/ctd.2017.3468 ◽

2017 ◽

Author(s):

Glauber De Bona

Keyword(s):

Knowledge Bases ◽

Probabilistic Logic ◽

Gambling Behaviour ◽

Dutch Books ◽

Probabilistic Knowledge ◽

Probabilistic Beliefs ◽

Inconsistent Knowledge ◽

Rationality Postulates

In AI, inconsistency measures have been proposed as a way to manage inconsistent knowledge bases. This work investigates inconsistency measuring in probabilistic logic. We show that previously existing rationality postulates for inconsistency measures in probabilistic knowledge bases are themselves incompatible and introduce a new way of localising inconsistency to reconcile these postulates. We then show the equivalence between distance-based inconsistency measures, from the AI community, and incoherence measures, from philosophy, that are based on the disadvantageous gambling behaviour entailed by incoherent probabilistic beliefs (via Dutch books). This provides a meaningful interpretation to the former and efficient methods to compute the latter.

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On Probabilistic Logical Argumentation

10.3233/faia210111 ◽

2021 ◽

Author(s):

Pilar Dellunde ◽

Lluís Godo ◽

Amanda Vidal

Keyword(s):

Conditional Probability ◽

Knowledge Bases ◽

Probabilistic Logic ◽

Abstract Argumentation ◽

Probabilistic Knowledge ◽

Consistency Properties

In this paper, we introduce a framework for probabilistic logic-based argumentation inspired on the DeLP formalism and an extensive use of conditional probability. We define probabilistic arguments built from possibly inconsistent probabilistic knowledge bases and study the notions of attack, defeat and preference between these arguments. Finally, we discuss consistency properties of admissible extensions of the Dung’s abstract argumentation graphs obtained from sets of probabilistic arguments and the attack relations between them.

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An Improved Set-based Reasoner for the Description Logic 𝒟ℒD4,×†

Fundamenta Informaticae ◽

10.3233/fi-2021-2009 ◽

2021 ◽

Vol 178 (4) ◽

pp. 315-346

Author(s):

Domenico Cantone ◽

Marianna Nicolosi-Asmundo ◽

Daniele Francesco Santamaria

Keyword(s):

Semantic Web ◽

Set Theory ◽

Description Logic ◽

Knowledge Bases ◽

Query Answering ◽

Conjunctive Query ◽

Classification Problems ◽

Previous Version ◽

Decidable Fragment ◽

Stratified Set

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D) (𝒟ℒD4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟ℒD4,×. In particular, it solves the consistency and the classification problems for 𝒟ℒD4,×-knowledge bases represented in set-theoretic terms, and a generalization of the Conjunctive Query Answering problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and improves a previous version, is implemented in C++. It supports 𝒟ℒD4,×-knowledge bases serialized in the OWL/XML format and it admits also rules expressed in SWRL (Semantic Web Rule Language).

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