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Quantified Temporal Alethic Boulesic Doxastic Logic
Stockholm University, Faculty of Humanities, Department of Philosophy.
2021 (English)In: Logica Universalis, ISSN 1661-8297, E-ISSN 1661-8300, Vol. 15, no 1, p. 1-65Article in journal (Refereed) Published
Abstract [en]

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a 'quantified' part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of T x W models, and the proof-theoretical apparatus of semantic tableaux. The 'quantified part' of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to `boulesic logic' (the logic of the will), 'willing' (`consenting', 'rejecting', 'indifference' and 'non-indifference') is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats 'believing' (and `conceiving') as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper.

Place, publisher, year, edition, pages
2021. Vol. 15, no 1, p. 1-65
Keywords [en]
Quantified modal logic, Modal logic, Temporal logic, Boulesic logic, Doxastic logic, Semantic tableaux
National Category
Philosophy, Ethics and Religion
Identifiers
URN: urn:nbn:se:su:diva-188150DOI: 10.1007/s11787-020-00264-zISI: 000587105300001OAI: oai:DiVA.org:su-188150DiVA, id: diva2:1513918
Available from: 2021-01-03 Created: 2021-01-03 Last updated: 2022-02-25Bibliographically approved

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Rönnedal, Daniel

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