Andreas Herzig

Propositional belief base update and minimal change

Abstract In this paper we examine ten concrete propositional update operations of the literature. We start by completely characterizing their relative strength and their computational complexity. Then we evaluate the competing update operations with respect to the postulates proposed by Katsuno and Mendelzon. It turns out that the majority violates most of the postulates. We argue that all violated postulates are undesirable except one. After that we evaluate the update operations with respect to another property which has been investigated extensively in the literature, viz. that disjunctive updates should not be identified with the exclusive disjunction. We argue that this is desirable, and show that the argument gives further support to the rejection of two of the postulates. Finally we study how the different approaches accommodate general laws governing the world, alias integrity constraints. Summing up our results, we conclude that only two of the update operations are satisfactory.

‘KNOWABLE’ AS ‘KNOWN AFTER AN ANNOUNCEMENT’

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ♦ϕ expresses that there is a truthful announcement ψ after which ϕ is true. This logic gives a perspective on Fitch’s knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.

A modal analysis of possibility theory

In this paper we study possibility theory from the point of view of modal logic. Our first and main result is that the logic of qualitative possibility is nothing else than Lewiss conditional logic VN. Second, we propose a multi-modal logic able to support possibility theory. Some connexions between these formalisms are stressed.

A logical formalization of the OCC theory of emotions

In this paper, we provide a logical formalization of the emotion triggering process and of its relationship with mental attitudes, as described in Ortony, Clore, and Collins’s theory. We argue that modal logics are particularly adapted to represent agents’ mental attitudes and to reason about them, and use a specific modal logic that we call Logic of Emotions in order to provide logical definitions of all but two of their 22 emotions. While these definitions may be subject to debate, we show that they allow to reason about emotions and to draw interesting conclusions from the theory.

A logic of intention and attempt

We present a modal logic called

ALTERNATIVE AXIOMATICS AND COMPLEXITY OF DELIBERATIVE STIT THEORIES

{\mathcal{LIA}}

What can we achieve by arbitrary announcements?: A dynamic take on Fitch's knowability

(logic of intention and attempt) in which we can reason about intention dynamics and intentional action execution. By exploiting the expressive power of