Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

Measuring Inconsistency over Sequences of Business Rule Cases

We investigate inconsistency and culpability measures for multisets of business rule bases. As companies might encounter thousands of rule bases daily, studying not only individual rule bases separately, but rather also their interrelations, becomes necessary. As current works on inconsistency measurement focus on assessing individual rule bases, we therefore present an extension of those works in the domain of business rules management. We show how arbitrary culpability measures (for single rule bases) can be automatically transformed for multisets, propose new rationality postulates for this setting, and investigate the complexity of central aspects regarding multi-rule base inconsistency measurement.

General information spaces: measuring inconsistency, rationality postulates, and complexity

AI systems often need to deal with inconsistent information. For this reason, since the early 2000s, some AI researchers have developed ways to measure the amount of inconsistency in a knowledge base. By now there is a substantial amount of research about various aspects of inconsistency measuring. The problem is that most of this work applies only to knowledge bases formulated as sets of formulas in propositional logic. Hence this work is not really applicable to the way that information is actually stored. The purpose of this paper is to extend inconsistency measuring to real world information. We first define the concept ofgeneral information spacewhich encompasses various types of databases and scenarios in AI systems. Then, we show how to transform any general information space to aninconsistency equivalentpropositional knowledge base, and finally apply propositional inconsistency measures to find the inconsistency of the general information space. Our method allows for the direct comparison of the inconsistency of different information spaces, even though the data is presented in different ways. We demonstrate the transformation on four general information spaces: a relational database, a graph database, a spatio-temporal database, and a Blocks world scenario, where we apply several inconsistency measures after performing the transformation. Then we review so-called rationality postulates that have been developed for propositional knowledge bases as a way to judge the intuitive properties of these measures. We show that although general information spaces may be nonmonotonic, there is a way to transform the postulates so they can be applied to general information spaces and we show which of the measures satisfy which of the postulates. Finally, we discuss the complexity of inconsistency measures for general information spaces.

Automated Comparative Study of Some Generalized Rough Approximations

The paper contains some remarks on building automated counterpart of a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to arbitrary binary relation. Our focus was on translating rationality postulates for such operators by means of the Mizar system – the software and the database which allows for expressing and checking mathematical knowledge for the logical correctness. The main objective was the formal (and machine-checked) proof of Theorem 4.1 from A. Gomolińska’s paper “A Comparative Study of Some Generalized Rough Approximations”, hence the present title. We provide also the discussion on how to make the presentation more efficient to reuse the reasoning techniques of the Mizar verifier.

Deductive and abductive argumentation based on information graphs

In this paper, we propose an argumentation formalism that allows for both deductive and abductive argumentation, where ‘deduction’ is used as an umbrella term for both defeasible and strict ‘forward’ inference. Our formalism is based on an extended version of our previously proposed information graph (IG) formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. In the current version, we consider additional types of information such as abstractions which allow domain experts to be more expressive in stating their knowledge, where we identify and impose constraints on the types of inferences that may be performed with the different types of information. A new notion of attack is defined that captures a crucial aspect of abductive reasoning, namely that of competition between abductively inferred alternative explanations. Our argumentation formalism generates an abstract argumentation framework and thus allows arguments to be formally evaluated. We prove that instantiations of our argumentation formalism satisfy key rationality postulates.

Belief Merging Operators as Maximum Likelihood Estimators

We study how belief merging operators can be considered as maximum likelihood estimators, i.e., we assume that there exists a (unknown) true state of the world and that each agent participating in the merging process receives a noisy signal of it, characterized by a noise model. The objective is then to aggregate the agents' belief bases to make the best possible guess about the true state of the world. In this paper, some logical connections between the rationality postulates for belief merging (IC postulates) and simple conditions over the noise model under consideration are exhibited. These results provide a new justification for IC merging postulates. We also provide results for two specific natural noise models: the world swap noise and the atom swap noise, by identifying distance-based merging operators that are maximum likelihood estimators for these two noise models.

A Fully Rational Account of Structured Argumentation Under Resource Bounds

ASPIC+ is an established general framework for argumentation and non-monotonic reasoning. However, ASPIC+ does not satisfy the non-contamination rationality postulates, and moreover, tacitly assumes unbounded resources when demonstrating satisfaction of the consistency postulates. In this paper we present a new version of ASPIC+ – Dialectial ASPIC+ – that is fully rational under resource bounds.

Proportional Belief Merging

In this paper we introduce proportionality to belief merging. Belief merging is a framework for aggregating information presented in the form of propositional formulas, and it generalizes many aggregation models in social choice. In our analysis, two incompatible notions of proportionality emerge: one similar to standard notions of proportionality in social choice, the other more in tune with the logic-based merging setting. Since established merging operators meet neither of these proportionality requirements, we design new proportional belief merging operators. We analyze the proposed operators against established rationality postulates, finding that current approaches to proportionality from the field of social choice are, at their core, incompatible with standard rationality postulates in belief merging. We provide characterization results that explain the underlying conflict, and provide a complexity analysis of our novel operators.

A Framework for Measuring Information Asymmetry

Information asymmetry occurs when an imbalance of knowledge exists between two parties, such as a buyer and a seller, a regulator and an operator, and an employer and an employee. It is a key concept in several domains, in particular, in economics. We propose in this work a general logic-based framework for measuring the information asymmetry between two parties. A situation of information asymmetry is represented by a knowledge base and a set of questions. We define the notion of information asymmetry measure through rationality postulates. We further introduce a syntactic concept, called minimal question subset (MQS), to take into consideration the fact that answering some questions allows avoiding others. This concept is used for defining rationality postulates and measures. Finally, we propose a method for computing the MQSes of a given situation of information asymmetry.

A Comparative Study of Some Central Notions of ASPIC+ and DeLP

This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud’s rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then ’s DeLP notion of warrant and ASPIC+ ’s notion of justification are equivalent. This result is proven for three alternative definitions of attack.