Quantified temporal alethic boulesic doxastic logic
type: Item
instance of: scholarly article
title: Quantified temporal alethic boulesic doxastic logic
zbMATH Open document ID: 1493.03003
author: Daniel Rönnedal
published in: Logica Universalis
publication date: 2021-05-05T00:00:00Z
review text: The paper presents a very rich version of the first-order modal language. The language includes four different groups of modalities which can be described as follows: \begin{itemize} \item Alethic modalities: necessity and possibility plus universal modality and its associated dual, the universal possibility. \item Temporal modalities: sometimes (resp. always) in the future (resp. in the past). Plus the absolute modalities of sometimes and always. The latter are not definable in terms of past and future since it is not generally assumed that any two given moments are comparable in terms of the temporal order. \item Doxastic modalities: believing and conceiving. \item So-called boulesic modalities: wanting, accepting, rejecting, and being indifferent. \end{itemize} The language also includes the equality predicate plus the special designated unary predicates \(R\) for being rational and \(E\) for existing. The language is supplied with a sort of Kripke semantics where the domain of (possible) objects is assumed to be constant. Beside the object domains, the models include the set of worlds and the set of time moments, and the formulas get evaluated at world-moment pairs. The models include a set of modal accessibility relations corresponding to the different groups of modalities allowed in the language. Whereas the temporal relation is given in the usual format, the alethic modal accessibility relation is ternary with the tuple of arguments of the form \((\mathrm{World}, \mathrm{World}, \mathrm{Moment})\), so that one world can be alethically accessible from another one at a particular time moment. In case of boulesic and doxastic accessibility relations, the argument tuple is even quaternary and has the form \((\mathrm{Object}, \mathrm{World}, \mathrm{World}, \mathrm{Moment})\). The object argument plays the role of the agent index since in the present setting the agents live as objects in the domain assigned to a given world. The author does not offer much in terms…
reviewed by: Grigory Olkhovikov
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03B44
zbMATH DE Number: 7344022
zbMATH Keywords: quantified modal logic
zbMATH Keywords: modal logic
zbMATH Keywords: temporal logic
zbMATH Keywords: boulesic logic
zbMATH Keywords: doxastic logic
zbMATH Keywords: semantic tableaux
MaRDI profile type: Publication
full work available at URL: s11787-020-00264-z
OpenAlex ID: W3096705509
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Quantified temporal alethic boulesic doxastic logic (DOI)
DOI: 10.1007/S11787-020-00264-Z