Reasons to Believe in a Social Environment

PRIMA 2017: Principles and Practice of Multi-Agent Systems, 2017

We present a logic for reasoning about the interplay between belief, evidence and trust in a multi-agent setting. We call this logic DL-BET which stands for "Dynamic Logic of Belief, Evidence and Trust". According to DL-BET, if the amount of evidence in support a given fact ϕ and the ratio of evidence in support of ϕ to the total amount of evidence in support of either ϕ or its negation are sufficient then, as a consequence, one should be willing to believe ϕ. We provide a sound and complete axiomatization for the logic and illustrate its expressive power with the aid of a concrete example.

2016

In this paper we focus on the formal qualitative representation of an agent’s evidence and justification in support of her beliefs and knowledge. Our formal setting is based on ‘justification models’, which we introduce as a generalization of the so-called ‘evidence models’ proposed by J. van Benthem and E. Pacuit in [18]. We use these structures to express how an agent’s evidence supports her doxastic state, expressing as such an agent’s justifiable beliefs. We study a number of specific classes of justification models as well as their relations. Overall, these structures are more general than the so-called plausibility models used to represent an agent’s doxastic and epistemic states in [14,7,8]. We illustrate the models in this paper via examples and focus on the dynamics of justification models.

The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.

Studia Logica, 2011

2012

We present a logic for reasoning about the evidence-based knowledge and beliefs and the evidential dynamics of non-logically-omniscient agents. We do this by adapting key tools and techniques from Dynamic Epistemic Logic, Justification Logic, and Belief Revision so as to provide a lightweight, yet fine-grained approach that characterizes well-known epistemic and doxastic attitudes in terms of the evidential reasoning that justifies these attitudes. We then add the dynamic operations of evidence introduction, evidence-based inference, strong acceptance of new evidence (evidential " upgrade "), and irrevocable acceptance of additional evidence (evidential " update "). We exemplify our theory by providing a formal dynamic account of Lehrer's well-known Gettier-type scenario involving the famous Ferrari and the infamous Messrs. Nogot and Havit.

It is a fact of life that we cannot believe everything we observe or that we are told. We accept a given information or datum as a belief on the basis of our previous beliefs, of its evidences, supports and sources, and of others psychological factors. Here I will sketch some crucial points of these cognitive mechanisms. Our knowledge base is not a file where one can introduce new data or eliminate a file-card without altering the other data. Our beliefs are integrated, interconnected and mutually supported: to drop a belief or to add a new one entails checking its coherence with other beliefs and revising previous knowledge. The belief-belief coherence and support is quite a well studied problem in philosophy and AI (truth maintenance systems; belief revision and updating; argumentation) and in some cognitive agent architectures. There are in fact two schools in belief revision (Harman 1986; Gärdenfors 1988; Doyle 1992): the foundations approach; stressing the importance of supports and justifications of beliefs, and the coherence approach; modelling logical compatibility and coherence. However, we agree with Doyle (1992) that there is no incompatibility between the two models, and that beliefs must be both relatively coherent and justified.

2014

We present a complete, decidable logic for reasoning about a notion of completely trustworthy (" conclusive ") evidence and its relations to justifiable (implicit) belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and " goodness " of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemov's Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness logics to provide an account for explicitly justified (defeasible) knowledge based on conclusive evidence that addresses the problem of (logical) omniscience.

2010

Justification Logic is a framework for reasoning about evidence and justification. Public Announcement Logic is a framework for reasoning about belief changes caused by public announcements. This paper develops JPAL, a dynamic justification logic of public announcements that corresponds to the modal theory of public announcements due to Gerbrandy and Groeneveld. JPAL allows us to reason about evidence brought about by and changed by Gerbrandy-Groeneveld-style public announcements.

Journal of Applied Logic, 2014

Bayesians understand the notion of evidential support in terms of probability raising. Little is known about the logic of the evidential support relation, thus understood. We investigate a number of prima facie plausible candidate logical principles for the evidential support relation and show which of these principles the Bayesian evidential support relation does and which it does not obey. We also consider the question which of these principles hold for a stronger notion of evidential support.

2015

This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief revision theory and dynamic-epistemic logics of information-driven agency. After describing the basic background, we review logics of various kinds of beliefs based on plausibility models, and then go on to various sorts of belief change engendered by changes in current models through hard and soft information. We present matching complete logics with dynamic-epistemic recursion axioms, and develop a very general perspective on belief change by the use of event models and priority update. The chapter continues with three topics that naturally complement the setting of single steps of belief change: connections with probabilistic approaches to belief change, long-term temporal process structure including links with formal learning theory, and multi-agent scenarios of information flow and belief revision in games and social networks. We end with a discussion of alternative approaches, further directions, and windows to the broader literature, while links with relevant philosophical traditions are discussed throughout.