Propositional Relevance through Letter-Sharing: Review and Contribution

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical form, known as its finest splitting. In this paper we explain these ideas; relate the approaches of Rodrigues and Parikh to each other; and briefly report some recent results of Kourousias and Makinson on the extent to which AGM belief change operations respect relevance. Finally we suggest a further refinement of the notion of relevance by introducing a parameter that allows one to take epistemic as well as purely logical components into account

Propositional relevance through letter-sharing

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into a canonical form, called its finest splitting. In the first part of this paper, we recall the ideas of Rodrigues and Parikh, and show that they yield equivalent definitions of what may be called canonical cell/path relevance. The second part presents the main new result of the paper: while the relation of canonical relevance is syntax-independent in the usual sense of the term, it nevertheless remains language-dependent in a deeper sense, as is shown with an example. The final part of the paper turns to questions of application, where we present a new concept of parameter-sensitive relevance that relaxes the Rodrigues/Parikh definition, allowing it to take into account extra-logical sources as well as purely logical ones

Semantic interpolation

We treat interpolation for various logics

Respecting relevance in belief change

En este trabajo dedicado a Carlos Alchourrón consideramos un problema que surgió recién después de su muerte en 1996 pero que seguramente habría sido de gran interés para él: ¿hasta dónde las operaciones formales sobre el cambio de creencias de AGM respetan el criterio de relevancia? Un criterio natural (aunque discutible) ha sido propuesto en 1999 por Rohit Parikh quien asimismo observó que el modelo AGM no siempre lo respeta. Nosotros discutimos los pros y los contras de este criterio y explicamos cómo podría refinarse AGM para que, si así lo deseáramos, lo respetara siempre.En este trabajo dedicado a Carlos Alchourrón consideramos un problema que surgió recién después de su muerte en 1996 pero que seguramente habría sido de gran interés para él: ¿hasta dónde las operaciones formales sobre el cambio de creencias de AGM respetan el criterio de relevancia? Un criterio natural (aunque discutible) ha sido propuesto en 1999 por Rohit Parikh quien asimismo observó que el modelo AGM no siempre lo respeta. Nosotros discutimos los pros y los contras de este criterio y explicamos cómo podría refinarse AGM para que, si así lo deseáramos, lo respetara siempre

Cooperative Replies to Unbelievable Assertions : A Dialogue Protocol Based on Logical Interpolation

Extended version of a paper with the same title presented at the Third International Conference on Agents and Artificial Intelligence (ICAART’11)We propose a dialogue protocol for situations in which an agent makes to another agent an assertion that the other agent finds impossible to believe. In this interaction, unbelievable assertions are rejected using explanations formed by logical interpolation and new assertions are being made such that all previous rebuttals are taken into account.Peer reviewe

A Simple Separation Logic

International audienceThe kinds of models that are usually considered in separation logic are structures such as words, trees, and more generally pointer structures (heaps). In this paper we introduce the separation logic of much simpler structures, viz. sets. The models of our set separation logic are nothing but valuations of classical propositional logic. Separating a valuation V consists in splitting it up into two partial valuations v 1 and v 2. Truth of a formula φ 1 * φ 2 in a valuation V can then be defined in two different ways: first, as truth of φ 1 in all total extensions of v 1 and truth of φ 2 in all total extensions of v 2; and second, as truth of φ 1 in some total extension of v 1 and truth of φ 2 in some total extension of v 2. The first is an operator of separation of resources: the update of φ 1 * φ 2 by ψ is the conjunction of the update of φ 1 by ψ and the update of φ 2 by ψ; in other words, φ 1 * φ 2 can be updated independently. The second is an operator of separation of processes: updates by ψ 1 * ψ 2 can be performed independently. We show that the satisfiability problem of our logic is decidable in polynomial space (PSPACE). We do so by embedding it into dynamic logic of propositional assignments (which is PSPACE complete). We moreover investigate its applicability to belief update and belief revision, where the separation operators allow to formulate natural requirements on independent pieces of information

Knowledge-based systems and geological survey

This personal and pragmatic review of the philosophy underpinning methods of geological surveying suggests that important influences of information technology have yet to make their impact. Early approaches took existing systems as metaphors, retaining the separation of maps, map explanations and information archives, organised around map sheets of fixed boundaries, scale and content. But system design should look ahead: a computer-based knowledge system for the same purpose can be built around hierarchies of spatial objects and their relationships, with maps as one means of visualisation, and information types linked as hypermedia and integrated in mark-up languages. The system framework and ontology, derived from the general geoscience model, could support consistent representation of the underlying concepts and maintain reference information on object classes and their behaviour. Models of processes and historical configurations could clarify the reasoning at any level of object detail and introduce new concepts such as complex systems. The up-to-date interpretation might centre on spatial models, constructed with explicit geological reasoning and evaluation of uncertainties. Assuming (at a future time) full computer support, the field survey results could be collected in real time as a multimedia stream, hyperlinked to and interacting with the other parts of the system as appropriate. Throughout, the knowledge is seen as human knowledge, with interactive computer support for recording and storing the information and processing it by such means as interpolating, correlating, browsing, selecting, retrieving, manipulating, calculating, analysing, generalising, filtering, visualising and delivering the results. Responsibilities may have to be reconsidered for various aspects of the system, such as: field surveying; spatial models and interpretation; geological processes, past configurations and reasoning; standard setting, system framework and ontology maintenance; training; storage, preservation, and dissemination of digital records

TOPIC SENSITIVE BELIEF REVISION

When asked to change one's beliefs in the face of new information, or to revise a book given errata, we commonly strive to keep our changes relevant, that is, we try to restrict the beliefs (or chapters) we change to those that bear some content relation to the new information. One kind of relevance, topicality, is interesting for two reasons: First, topicality tends to be strongly encapsulating, e.g., we shouldn't make any off-topic changes. Second, topicality tends to be weaker than strict relevance. Consider a panel of three papers on the topic of Kant's life and works. It would be entirely possible for each of the papers to have no bearing on the truth of any sentence in any of the other papers, and yet for all of the papers to be on topic. In this dissertation, I explore theories of logical topicality and their effect on formal theories of belief revision. Formal theories of belief revision (in the Alchourrón, Gärdenfors, and Makinson (AGM) tradition) model the object of change (my beliefs, a book) as a collection of formulae in a supra-classical logic and provide a set of postulates which express constraints on the sorts of change that are, in principle, formally rational. In 1999, Rohit Parikh proposed that signature disjointness captured a reasonable notion of topicality but that taking topicality into account required changes in the standard AGM postulates (and thus, the notion of rational change). He, and subsequent theorists, abandoned this notion of topicality in order to deal with the revision of inconsistent objects of change. In this thesis, I show 1) that a disjoint signature account of topicality does not require changes to the AGM rationality postulates and 2) a disjoint signature account of topicality can apply to inconsistent objects of change. Additionally, I argue that signature disjointness has a strong claim to being at least a sufficient condition of logical topicality