Dragan Doder

Measures of inconsistency and defaults

We introduce a method for measuring inconsistency based on the number of formulas needed for deriving a contradiction. The relationships to previously considered methods based on probability measures are discussed. Those methods are extended to conditional probability and default reasoning.

Probabilistic Abstract Dialectical Frameworks

Although Dungs frameworks are widely approved tools for abstract argumentation, their abstractness makes expressing notions such as support or uncertainty very difficult. Thus, many of their generalizations were created, including the probabilistic argumentation frameworks (PrAFs) and the abstract dialectical frameworks (ADFs). While the first allow modeling uncertain arguments and attacks, the latter can handle various dependencies between arguments. Although the actual probability layer in PrAFs is independent of the chosen semantics, new relations pose new challenges and new interpretations of what is the probability of a relation. Thus, the methodology for handling uncertainties cannot be shifted to more general structures without any further thought. In this paper we show how ADFs are extended with probabilities.

A Probabilistic Temporal Logic That Can Model Reasoning about Evidence

The aim of the paper is to present a sound, strongly complete and decidable probabilistic temporal logic that can model reasoning about evidence.

Probabilistic Argumentation Frameworks --- A Logical Approach

Abstract argumentation is nowadays a vivid field within artificial intelligence and has seen different developments recently. In particular, enrichments of the standard Dung frameworks have been proposed in order to model scenarios where probabilities or uncertain information have to be expressed. As for standard approaches of abstract argumentation, a uniform logical formalization for such frameworks is of great help in order to understand and compare different approaches. In this paper, we take a first step in this direction and characterize different semantics from the approach of Li et al in terms of probabilistic logic. This not only provides a uniform logical formalization but also might pave the way for future implementations.

Probabilistic logics for objects located in space and time

Spatiotemporal databases can be used to efficiently store and retrieve information about objects moving in space and time. Probabilities are added to model the case where the locations are not known with certainty. A few years ago a new formalism was introduced to represent such information in the form of atomic formulas, each of which represents the probability (in the form of an interval because even the probabilities are not known precisely) that a particular object is in a particular location at a particular time. We extend this formalism to obtain several different probabilistic logics by adding logical operators. Furthermore, we axiomatize these logics, provide corresponding semantics, prove that the axiomatizations are sound and complete, and discuss decidability issues. While we relate these logics to previous axiomatizations of probabilistic logics, this article is self-contained: no prior knowledge of probabilistic logics is assumed.

A logic with conditional probability operators

This paper presents a sound and strongly complete axiomatization of the reasoning about linear combinations of conditional probabilities, including compar- ative statements. The developed logic is decidable, with a PSPACE containment for the decision procedure.

A propositional probabilistic logic with discrete linear time for reasoning about evidence

The aim of the paper is to present a sound, strongly complete and decidable probabilistic temporal logic that can model reasoning about evidence. The formal system developed here is actually a solution of a problem proposed by Halpern and Pucella (J Artif Intell Res 26:1–34, 2006).

Acceptability Semantics for Weighted Argumentation Frameworks

The paper studies semantics for evaluating arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

Probabilistic approach to nonmonotonic consequence relations

The paper offers a probabilistic characterizations of determinacy preservation, fragmented disjunction and conditional excluding middle for preferential relations. The paper also presents a preferential relation that is above Disjunctive rationality and strictly below Rational monotonicity. This so called ɛ, µ-relation is constructed using a positive infinitesimal e and a finitely additive hyperreal valued probability measure µ on the set of propositional formulas.

Probabilistic Logics with Independence and Confirmation

The main goal of this work is to present the proof-theoretical and model-theoretical approaches to probabilistic logics which allow reasoning about independence and probabilistic support. We extend the existing formalisms [14] to obtain several variants of probabilistic logics by adding the operators for independence and confirmation to the syntax. We axiomatize these logics, provide corresponding semantics, prove that the axiomatizations are sound and strongly complete, and discuss decidability issues.