Forgetting complex propositions

This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition $\pi$ is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this. We resolve this situation by considering expressions of the form $[\boldsymbol{\ddagger} \pi]\varphi$, which quantify over all possible (but minimal) ways of forgetting whether $\pi$. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets $\pi$ (rather than forgets whether $\pi$) and when the modification of atomic facts is done non-uniformly throughout the model

Four Logics for Minimal Belief Revision

It is natural to think of belief revision as the interaction of belief and information over time. Thus branching-time temporal logic seems a natural setting for a theory of belief revision. We propose a logic based on three modal operators: a belief operator, an information operator and a next-time operator. Four logics of increasing strength are proposed. The first is a logic that captures the most basic notion of minimal belief revision. The second characterizes the qualitative content of Bayes' rule. The third provides an axiomatization of the AGM theory of belief revision and the fourth provides a characterization of the notion of plausibility ordering of the set of possible worlds.

Preference-Dependent Unawareness

Morris (1996, 1997) introduced preference-based definitions of knowledge of belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is behaviorally characterized as the event being null and its negation being null.Unawareness, awareness, knowledge, preferences, subjective expected utility theory, decision theory, null event

Preference-Based Unawareness

Morris (1996, 1997) introduced preference-based definitions of knowledge of belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is behaviorally characterized as the event being null and its negation being null.unawareness, awareness, knowledge, preferences, subjective expected utility theory, decision theory, null event

Axiomatization of the AGM theory of belief revision in a temporal logic

It is natural to think of belief revision as the interaction of belief and information over time. Thus branching-time temporal logic seems a natural setting for a theory of belief revision. We propose two extensions of a modal logic that, besides the ""next-time"" temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatization of the full set of AGM postulates.Belief revision, information, temporal logic, AGM theory

Semantic structures for one-stage and iterated belief revision

Semantic structures for belief revision and iterated belief revision are proposed. We start with one-stage revision structures that generalize the notion of choice function from rational choice theory. A correspondence between these one-stage structures and AGM belief revision functions is established. We then add branching time and consider more general structures that accommodate iterated revision. AGM temporal belief revision structures are defined and a syntactic axiomatization is provided

Dynamic-Epistemic reasoning on distributed systems

We propose a new logic designed for modelling and reasoning about information flow and information exchange between spatially located (but potentially mobile), interconnected agents witnessing a distributed computation. This is a major problem in the field of distributed systems, covering many different issues, with potential applications from Computer Science and Economy to Chemistry and Systems Biology. Underpinning on the dual algebraical-coalgebraical characteristics of process calculi, we design a decidable and completely axiomatizad logic that combines the processalgebraical/ equational and the modal/coequational features and is developed for process-algebraical semantics. The construction is done by mixing operators from dynamic and epistemic logics with operators from spatial logics for distributed and mobile systems. This is the preliminary version of a paper that will appear in Proceedings of the second Conference on Algebra and Coalgebra in Computer Science (CALCO2007), LNCS 4624, Springer, 2007. The original publication is available at www.springerlink.co