A dynamic epistemic framework for reasoning about conformant probabilistic plans

In this paper, we introduce a probabilistic dynamic epistemic logical framework that can be applied for reasoning and verifying conformant probabilistic plans in a single agent setting. In conformant probabilistic planning (CPP), we are looking for a linear plan such that the probability of achieving the goal after executing the plan is no less than a given threshold probability δ. Our logical framework can trace the change of the belief state of the agent during the execution of the plan and verify the conformant plans. Moreover, with this logic, we can enrich the CPP framework by formulating the goal as a formula in our language with action modalities and probabilistic beliefs. As for the main technical results, we provide a complete axiomatization of the logic and show the decidability of its validity problem

Abstract rationality: the 'logical' structure of attitudes

We present an abstract model of rationality theories that focuses on structural properties of attitudes. We construe rationality as coherence between one's attitudes, e.g., one's beliefs, values, and intentions. We introduce three 'logical' conditions on attitudes: consistency, completeness, and closedness. They generalise the classic logical conditions on beliefs towards multiple attitudes, but contrast with standard rationality conditions such as transitivity for preferences, modus ponens for binary beliefs, additivity for probabilistic beliefs, and non-akrasia for intentions. We establish a formal correspondence between our three logical conditions and standard rationality conditions. Addressing John Broome's enquiry into the achievability of rationality through reasoning, we characterize the extent to which explicit reasoning can help one become more 'logical', i.e., acquire consistent, complete, or closed attitudes, respectively. Our analysis forms a bridge between rationality and logic, and enables logical talk about multi-attitude psychology

Group decision making via probabilistic belief merging

We propose a probabilistic-logical framework for group decision-making. Its main characteristic is that we derive group preferences from agents’ beliefs and utilities rather than from their individual preferences as done in social choice approaches. This can be more appropriate when the individual preferences hide too much of the individuals’ opinions that determined their preferences. We introduce three preference relations and investigate the relationships between the group preferences and in-dividual and subgroup preferences

The logic and pragmatics of the representation and alteration of beliefs.

In this thesis, I show the extent to which the distinction between logical rationality (the consistency with a set of assumptions) and pragmatic rationality (the strong tendency of providing benefits to actual agents) helps to make sense of probabilistic accounts of the representation and alteration of beliefs. In order to do this, I first show how the probabilistic representations of beliefs can be seen to follow on from the failure of the cogency of the Logical Theories of probability. I then move on to discuss the four classic theories of probabilistic representations of belief in the literature (those of Ramsey, de Finetti, Savage and Jeffrey) and a key modern treatment (that of Howson & Urbach). Thirdly, I continue the argument by discussing the two key justifications for the core account of the probabilistic alteration of beliefs - Bayesian Conditionalisation - to show that these arguments - if anything - only show the logical rationality of this way of altering beliefs, but not its pragmatic rationality. In a fourth step, I provide a novel justification of this sort by basing it on the tendency of Bayesian Conditionalisation to structure an agent's thoughts and decisions in a way that lowers her decision-making costs. I also discuss some of the consequences of such a justification for Bayesian Conditionalisation, in particular with a view to other conditionalisation principles like Jeffrey Conditionalisation. Finally, I point out some connections of this discussion to contemporary and traditional philosophy of science

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Probability Logic for Harsanyi Type Spaces

Probability logic has contributed to significant developments in belief types for game-theoretical economics. We present a new probability logic for Harsanyi Type spaces, show its completeness, and prove both a de-nesting property and a unique extension theorem. We then prove that multi-agent interactive epistemology has greater complexity than its single-agent counterpart by showing that if the probability indices of the belief language are restricted to a finite set of rationals and there are finitely many propositional letters, then the canonical space for probabilistic beliefs with one agent is finite while the canonical one with at least two agents has the cardinality of the continuum. Finally, we generalize the three notions of definability in multimodal logics to logics of probabilistic belief and knowledge, namely implicit definability, reducibility, and explicit definability. We find that S5-knowledge can be implicitly defined by probabilistic belief but not reduced to it and hence is not explicitly definable by probabilistic belief