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

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

On the proper treatment of context in NL

The proper treatment of quantification in Natural Language proposed by Richard Montague some thirty years ago does not do proper justice to the fact that interpretation of texts both uses context and sets up new contexts. The dynamic turn in NL semantics is the attempt to model this basic fact, but the use of dynamically quantified variables introduces an undesirable element into this attempt. By extending a variable free `incremental dynamics' with a flexible system of type scheme patterns and type scheme pattern matching, we arrive at a Montague style architecture for NL semantics that provides a proper treatment both of quantification and of context use and context change

Typed logics with states

The paper presents a simple format for typed logics with states by adding a function for register update to standard typed lambda calculus. It is shown that universal validity of equality for this extended language is decidable (extending a well-known result of Friedman for typed lambda calculus). This system is next extended to a full fledged typed dynamic logic, and it is illustrated how the resulting format allows for very simple and intuitive representations of dynamic semantics for natural language and denotational semantics for imperative programming. The proposal is compared with some alternative approaches to formulating typed versions of dynamic logics

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