Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Bimodal Logic
Stockholm University, Faculty of Humanities, Department of Philosophy.
2012 (English)In: Polish Journal of Philosophy, ISSN 1897-1652, E-ISSN 2154-3747, Vol. 6, no 2, 71-93 p.Article in journal (Refereed) Published
Abstract [en]

Many interesting philosophical principles include two kinds of modalities, e.g. epistemic and doxastic, alethic and epistemic, or alethic and deontic modalities. The purpose of this essay is to describe a set of bimodal systems, i.e. systems that include two kinds of modal operators, in which it is possible to investigate some formalizations of such principles. All in all we will consider 4,194,304 logics. All logics are described semantically and proof theoretically. We use possible world semantics to characterize the logics semantically and both axiomatic systems and semantic tableaux to characterize them proof theoretically. We show that all systems are sound and complete with respect to their semantics and we consider some relationships between the various systems.

Place, publisher, year, edition, pages
2012. Vol. 6, no 2, 71-93 p.
Keyword [en]
Bimodal logic, modal logic, epistemic logic, deontic logic, tense logic
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
URN: urn:nbn:se:su:diva-81229DOI: 10.5840/pjphil20126214OAI: oai:DiVA.org:su-81229DiVA: diva2:561982
Available from: 2012-10-22 Created: 2012-10-15 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Extensions of Deontic Logic: An Investigation into some Multi-Modal Systems
Open this publication in new window or tab >>Extensions of Deontic Logic: An Investigation into some Multi-Modal Systems
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Deontic logic is a branch of logic that deals with normative concepts, propositions, arguments and systems. The main purpose of this compilation thesis is to investigate how deontic logic can be extended in a number of ways. We consider several multimodal systems, i.e. systems that include more than one modality, e.g. deontic, alethic and temporal modalities. We also say something about some logics that include counterfactuals. The purpose of Paper I is to develop a class of semantic tableau systems for some counterfactual logics. We discuss 1024 systems. Soundness results are obtained for every tableau system and completeness results for a large subclass of these. In Paper II we describe a class of semantic tableau systems for some dyadic deontic logics. We consider 16 pure dyadic deontic systems and 32 alethic dyadic deontic systems. Soundness results are proved for every tableau system and completeness results are obtained for all 16 pure dyadic deontic systems and for 16 alethic dyadic deontic systems. In Paper III we consider several different interpretations of the concept of conditional obligation or commitment and we say something about its logical properties. Paper IV deals with several bimodal systems, i.e. systems that include two kinds of modal operators. Bimodal systems are interesting because many philosophical principles include two kinds of modalities, e.g. the ought-implies-can principle, the knowledge-implies-belief principle and the means-end principle. We study 4,194,304 bimodal logics and we use both axiomatic systems and semantic tableaux to characterize them proof theoretically. We show that all our axiomatic and tableau systems are sound and complete with respect to their semantics. The purpose of Paper V is to describe a set of 2,147,483,648 temporal alethic-deontic systems, i.e. systems that include temporal, alethic and deontic operators. We show that all systems are sound and complete with respect to their semantics.

Place, publisher, year, edition, pages
Stockholm: Department of Philosophy, Stockholm University, 2012. 150 p.
Keyword
Deontic logic, Modal logic, Dyadic deontic logic, Semantic tableau, Conditional obligation, Commitment, Counterfactuals, Multi-modal logic, Bimodal logic, Temporal logic, T x W logic, Ought-implies-can, The means-end principle
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
urn:nbn:se:su:diva-80803 (URN)978-91-7447-584-5 (ISBN)
Public defence
2012-12-08, D9, Universitetsvägen 10 D, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Submitted.

Available from: 2012-11-15 Created: 2012-09-28 Last updated: 2012-11-07Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Rönnedal, Daniel
By organisation
Department of Philosophy
In the same journal
Polish Journal of Philosophy
Philosophy

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 142 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf