Dynamic epistemic modelling

This paper introduces DEMO, a Dynamic Epistemic Modelling tool. DEMO llows modelling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, translation of dynamic epistemic formulas to PDL formulas, and so on. The paper implements a reduction of dynamic epistemic logic to PDL. The reduction of dynamic epistemic logic to automata PDL from Van Benthem and Kooi is also discussed and implemented. Epistemic models are minimized under bisimulation, and update action models are minimized under action emulation (the appropriate structural notion for having the same update effect). The paper is an exemplar of tool building for epistemic updatelogic. It contains the full code of an implementation in Haskell in `literate programming' style, of DEM

Perception and Change in Update Logic

Abstract Three key ways of updating one's knowledge are (i) perception of states of affairs, e.g., seeing with one's own eyes that something is the case, (ii) recep- tion of messages, e.g., being told that something is the case, and (iii) drawing new conclusions from known facts. If one represents knowledge by means of Kripke models, the implicit assumption is that drawing conclusions is immediate. This as- sumption of logical omniscience is a useful abstraction. It leaves the distinction between (i) and (ii) to be accounted for. In current versions of Update Logic (Dy- namic Epistemic Logic, Logic of Communication and Change) perception and mes- sage reception are not distinguished. This paper proposes an extension of Update Logic that makes this distinction explicit. The logic deals with three kinds of up- dates: announcements, changes of the world, and observations about the world in the presence of witnesses. The resulting logic is shown to be complete by means of a reduction to epistemic propositional dynamic logic by a well known method

Varieties of Belief and Probability

For reasoning about uncertain situations, we have probability theory, and we have logics of knowledge and belief. How does elementary probability theory relate to epistemic logic and the logic of belief? The paper focuses on the notion of betting belief, and interprets a language for knowledge and belief in two kinds of models: epistemic neighbourhood models and epistemic probability models. It is shown that the first class of models is more general in the sense that every probability model gives rise to a neighbourhood model, but not vice versa. The basic calculus of knowledge and betting belief is incomplete for probability models. These formal results were obtained in Van Eijck and Renne [9]

Yet More Modal Logics of Preference Change and Belief Revision

We contrast Bonanno's `Belief Revision in a Temporal Framework' \cite{Bonanno07:briatfTV} with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communic

Syllogistics = monotonicity + symmetry + existential import

Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into account. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantifiers, while completeness for syllogistic theory is proved by direct inspection of the valid syllogisms. Next, the valid syllogisms are decomposed in terms of the rules they involve. The implementation uses Haskell, and is given i

Dynamic reasoning without variables

A variable free notation for dynamic logic is proposed which takes its cue from De Bruijn's variable free notation for lambda calculus. De Bruijn indexing replaces variables by indices which indicate the distance to their binders. We propose to use reverse De Bruijn indexing, which works almost the same, only now the indices refer to the depth of the binding operator in the formula. The resulting system is analysed at length and applied to a new rational reconstruction of discourse representation theory. It is argued that the present system of dynamic logic without variables provides an explicit account of anaphoric context and yields new insight into the dynamics of anaphoric linking in reasoning. A calculus for dynamic reasoning with anaphora is presented and its soundness and completeness are established

Guarded actions

Guarded actions are changes with preconditions acting as a guard. Guarded action models are multimodal Kripke models with the valuations replaced by guarded actions. Call guarded action logic the result of adding product updates with guarded action models to PDL (propositional dynamic logic). We show that guarded action logic reduces to PD