Logical bases of modal navigation

Résumé 0

From the age of 4 a human being has prodigious skills in modal navigation, with the ability to extract himself/herself out of the present to travel at high speed in universes of possible worlds: past and future travel (mental time travel), fictional navigation (games, novels, movies, virtual reality…), epistemic navigation (mind-reading of other people's worlds), mind-wandering and fantasic life, esthetic travel (e.g., through pictorial or musical works), spiritual travel, and of course logical travel (a reasoning implies generally to consider multiple alternatives).However, while powerful formal tools, such as the semantics of possible worlds, have been forged for a long time to deal with inferences in modal logic, the logical bases of modal navigation remain little discussed. In order to advance in this direction, we will first specify the representational tools necessary for any modal navigation, based on the conceptual framework of representational spaces where a (universe of) world(s) is constituted from fragments of presence and links that allow to unify these fragments (such as Hypertext links associates pages on the word wide web) [1]. The notion of modal abstraction will be introduced as an operation allowing to modalize (and more generally to contextualize) a content fragment as belonging to a specific world (or more generally to a specific context), with marking by a symbol that refers a content to a specific world [2]. We will then specify the logical conditions for an adequate representation of the universes of possible worlds in modal navigation and will propose for this purpose a quantified modal language using terms of possible worlds. We will show that it is possible to account for navigational dynamics between worlds — with the inter-world tracking necessary for safe high-speed navigation — by implementing the world terms as nodes in an activation network [3].Finally, we will specify how modal navigation can serve as a paradigm for the general logical study of mental navigation, as a possible world can be considered mentally as a context-specific case.References[1] Plagnol, A. (2004). Espaces de représentation : théorie élémentaire et psychopathologie. Paris : Editions du CNRS.[2] Plagnol, A. (in press). Logic and theory of representation. In J.-Y. Beziau & A Moktefi (Eds.), Logic in question- 7. Springer.[3] Plagnol, A. (2019). Principes de navigation dans les mondes possibles — Tome 1 : Fondations. Paris : Editions Terra Cotta.