Generalized belief change with imprecise probabilities and graphical models

We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored

Opinions and Preferences as Socially Distributed Attitudes

The dissertation focuses on how to best represent the consensus and attitude dynamic of a group given the attitudes of its individuals. This is done in the Bayesian epistemology framework using pooling with imprecise probabilities, and in utility theory extending Harsanyi's aggregation theorem to characterize other directed attitudes like spite and altruism. The final part of the dissertation considers attitudes within social networks and provides explanations and simulation models for online segregation and tribalism as well as the spread of rumors through contagion. The dissertation hopes to contribute to foundational issues like that of epistemic consensus, but also to new emerging phenomena in social epistemology

Concept logics

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and the taxonomical hierarchies of the domain to be modeled. This paper addresses the combination of the fast taxonomical reasoning algorithms (e.g. subsumption, the classifier etc.) that come with these languages and reasoning in first order predicate logic. The interface between these two different modes of reasoning is accomplished by a new rule of inference, called constrained resolution. Correctness, completeness as well as the decidability of the constraints (in a restricted constraint language) are shown

A conditional perspective of belief revision

Belief Revision is a subarea of Knowledge Representation and Reasoning (KRR) that investigates how to rationally revise an intelligent agent's beliefs in response to new information. There are several approaches to belief revision, but one well-known approach is the AGM model, which is rooted in work by Alchourrón, Gärdenfors, and Makinson. This model provides a set of axioms defining desirable properties of belief revision operators, which manipulate the agent's belief set represented as a set of propositional formulas. A famous extension to the classical AGM framework of Belief Revision is Darwiche and Pearl's approach to iterated belief revision. They uncovered that the key to rational behavior under iteration is adequate preservation of conditional beliefs, i.e., beliefs the agent is willing to accept in light of (hypothetical) new information. Therefore, they introduced belief revision operators modifying the agent's belief state, built from conditional beliefs. Kern-Isberner fully axiomatized a principle of conditional preservation for belief revision, which captures the core of adequate treatment of conditional beliefs during the revision. This powerful axiom provides the necessary conceptual framework for revising belief states with sets of conditionals as input, and it shows that conditional beliefs are subtle but essential for studying the process of belief revision. This thesis provides a conditional perspective of Belief Revision for different belief revision scenarios. In the first part, we introduce and investigate a notion of locality for belief revision operators on the semantic level. Hence, we exploit the unique features of conditionals, which allow us to set up local cases and revise according to these cases, s.t., the complexity of the revision task is reduced significantly. In the second part, we consider the general setting of belief revision with respect to additional meta-information accompanying the input information. We demonstrate the versatility and flexibility of conditionals as input for belief revision operators by reducing the parameterized input to a conditional one for two well-known parameterized belief revision operators who are similarly motivated but very different in their technical execution. Our results show that considering conditional beliefs as input for belief revision operators provides a gateway to new insights into the dynamics of belief revision

Dynamic Aspects of Knowledge Bases

A knowledge base is considered a system that is told information about an external world and that answers questions about this world. Our goal here is to outline knowledge bases that involve both knowledge and beliefs. In previous studies, various kinds of belief change have been studied in isolation, but we want to tie them together. We aim at knowledge bases that could carry the epistemic states of agents, that is, the knowledge and the beliefs that an agent has at any one moment in time. The difference between knowledge and belief is that while knowledge increases monotonically with time, beliefs may at some later point in time turn out to be false. Beliefs may change for various reasons: in belief revision, beliefs are changed when receiving new information about a world that has not changed, while in belief update a change in the world is to be recorded. Different types of change call for different treatments. In belief-change studies, various change types have been characterized by rationality criteria set on each type. The main principles in these criteria are maintaining consistency of beliefs and minimality of change. When dealing with belief change, our approach is to take knowledge as an integrity constraint that should always hold, and we describe how the rationality criteria should be modified accordingly. In our refined rationality criteria, beliefs that are inconsistent with the knowledge of the knowledge base will never be allowed to enter into the knowledge base. In the rationality criteria, a common assumption is that the most recent information is the most reliable, and it has therefore been prioritized over the old beliefs. However, this may not be the case in all circumstances. In order to complete the collection of belief-change types, we propose a new, commutative type of change for entering competing evidence into the knowledge base. The representation theorems that have been given for belief revision indicate that belief revision involves an ordering of disbelief on possible alternative situations, or equivalently, an epistemic entrenchment on logical formulas. A formula less entrenched is more easily given up when eliminating inconsistancies. In view of the changes in the rationality criteria, we also refine the representation theorems. We introduce two finite representations for knowledge bases, one with a finite ordered set of propositional formulas that are satisfiable but pairwise inconsistent with each other, and the other with a finite list of pairwise inconsistent propositional formulas. Both representations involve dynamic orderings of disbelief that have arisen out of the previous change operations. We show that for the knowledge base to satisfy the rationality criteria given for belief revision, the dynamic ordering of disbelief in the knowledge base is vital. The representations and the operators that we introduce in this thesis demonstrate how this ordering of disbelief could be dealt with in various operations.Tietämyskanta on järjestelmä, joka vastaanottaa ulkomaailmaa koskevaa informaatiota ja vastaa sitä koskeviin kyselyihin. Tietämyskantaa muutetaan, kun ulkomaailmasta saadaan uutta informaatiota, tai kun halutaan rekisteröidä siellä tapahtunut muutos. Väitöskirjatyössä hahmotellaan tietämyskantoja, jotka sisältävät sekä tietoa että uskomuksia. Uskomukset voivat osoittautua virheellisiksi, jolloin niitä voidaan joutua korjaamaan tai päivittämään. Filosofit ovat luonnehtineet uskomusten korjaamista asettamillaan järkevyyskriteereillä. Erityyppisillä muutoksilla on omat kriteerinsä. Tässä väitöstyössä järkevyyskriteerejä muutetaan siten, että tietämyskantaan ei hyväksytä tiedon kanssa ristiriitaisia uskomuksia, sekä esitetään uusi, kommutatiivinen muutostyyppi, jossa viimeisintä informaatiota ei priorisoida. Lisäksi analysoidaan, millä oletuksilla uskomusten korjaamiseen aiemmin ehdotetut kriteerit ovat keskenään ristiriitaiset. Tässä väitöskirjassa on ollut tavoitteena hahmotella tietämyskanta kokonaisuutena, jossa eri tyyppiset muutokset voivat vuorotella. Tietämyskannalle esitetään esimerkinomaisesti kaksi toteutustapaa, määritellään niille muutosoperaattorit sekä osoitetaan, että operaattorit toteuttavat muutostyyppinsä järkevyyskriteerit

Dilemmas, Disagreement, and Dualism

This paper introduces and motivates a solution to a dilemma from peer disagreement. Following Buchak (2021), I argue that peer disagreement puts us in an epistemic dilemma: there is reason to think that our opinions should both change and not change when we encounter disagreement with our epistemic peers. I argue that we can solve this dilemma by changing our credences, but not our beliefs in response to disagreement. I explain how my view solves the dilemma in question, and then offer two additional arguments for it: one related to contents and attitudes, and another related to epistemic peerhood

Belief Revision in Expressive Knowledge Representation Formalisms

We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach