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Temporal alethic–deontic logic and semantic tableaux
Stockholm University, Faculty of Humanities, Department of Philosophy.
2012 (English)In: Journal of Applied Logic, ISSN 1570-8683, E-ISSN 1570-8691, Vol. 10, no 3, 219-237 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to describe a set of temporal alethic–deontic systems, i.e. systems that include temporal, alethic and deontic operators. All in all we will consider 2,147,483,648 systems. All systems are described both semantically and proof theoretically. We use a kind of possible world semantics, inspired by the so-called T ×W semantics, to characterize our systems semantically and semantic tableaux to characterize them proof theoretically. We also show that all systems are sound and complete with respect to their semantics.

Place, publisher, year, edition, pages
2012. Vol. 10, no 3, 219-237 p.
Keyword [en]
T×W logics, Temporal logic, Modal logic, Deontic logic, Semantic tableaux, Historical necessity, The ought-implies-can principle, The means-end principle
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
URN: urn:nbn:se:su:diva-77037DOI: 10.1016/j.jal.2012.03.002ISI: 000305772600001OAI: oai:DiVA.org:su-77037DiVA: diva2:529141
Available from: 2012-05-29 Created: 2012-05-29 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

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