scholarly journals On Probabilistic Logical Argumentation

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.

scholarly journals Implementing an Efficient SAT Solver for a Probabilistic Description Logic

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.

scholarly journals Measuring Inconsistency in Probabilistic Knowledge Bases

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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