Quantified Temporal Alethic Boulesic Doxastic Logic

Logica Universalis 15 (1):1-65 (2021)


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 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 $$T \times W$$ T × 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’, ‘willing’ is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ 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.

Download options


    Upload a copy of this work     Papers currently archived: 72,805

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

126 (#95,429)

6 months
21 (#42,234)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Daniel Rönnedal
Stockholm University

References found in this work

Past, present and future.Arthur Prior - 1967 - Revue Philosophique de la France Et de l'Etranger 157:476-476.
Tense and Reality.Kit Fine - 2005 - In Modality and Tense. Oxford University Press. pp. 261--320.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Bulletin of Symbolic Logic 14 (4):544-545.
On Logics of Knowledge and Belief.Robert Stalnaker - 2006 - Philosophical Studies 128 (1):169-199.

View all 72 references / Add more references

Similar books and articles

Boulesic-Doxastic Logic.Daniel Rönnedal - 2019 - Australasian Journal of Logic 16 (3):83.
Quantified Temporal Alethic-Deontic Logic.Daniel Rönnedal - 2014 - Logic and Logical Philosophy 24 (1):19-59.
Boulesic Logic, Deontic Logic and the Structure of a Perfectly Rational Will.Daniel Rönnedal - 2020 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 27 (2):187–262.
Quantified Counterfactual Temporal Alethic-Deontic Logic.Daniel Rönnedal - 2017 - South American Journal of Logic 3 (1):145–172.
Counterfactuals in Temporal Alethic-Deontic Logic.Rönnedal Daniel - 2016 - South American Journal of Logic 2 (1):57-81.
Temporal Alethic–Deontic Logic and Semantic Tableaux.Daniel Rönnedal - 2012 - Journal of Applied Logic 10 (3):219-237.
Doxastic Logic: A New Approach.Daniel Rönnedal - 2018 - Journal of Applied Non-Classical Logics 28 (4):313-347.
Bimodal Logic.Daniel Rönnedal - 2012 - Polish Journal of Philosophy 6 (2):71-93.
Dyadic Deontic Logic and Semantic Tableaux.Daniel Rönnedal - 2009 - Logic and Logical Philosophy 18 (3-4):221-252.
Investigations Into Quantified Modal Logic.Yannis Stephanou - 2002 - Notre Dame Journal of Formal Logic 43 (4):193-220.
Dynamic Tableaux for Dynamic Modal Logics.Jonas De Vuyst - 2013 - Dissertation, Vrije Universiteit Brussel
Relational Dual Tableaux for Interval Temporal Logics.David Bresolin, Joanna Golinska-Pilarek & Ewa Orlowska - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):251–277.
‘Now’ and ‘Then’ in Tense Logic.Ulrich Meyer - 2009 - Journal of Philosophical Logic 38 (2):229-247.