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Extensions of Deontic Logic: An Investigation into some Multi-Modal Systems
Stockholm University, Faculty of Humanities, Department of Philosophy.
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 [en]
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: urn:nbn:se:su:diva-80803ISBN: 978-91-7447-584-5 (print)OAI: oai:DiVA.org:su-80803DiVA: diva2:561984
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
List of papers
1. Counterfactuals and Semantic Tableaux
Open this publication in new window or tab >>Counterfactuals and Semantic Tableaux
2009 (English)In: Logic and logical philosophy, ISSN 1425-3305, Vol. 18, no 1, 71-91 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to develop a class of semantic tableau systems for some counterfactual logics. All in all I will discuss 1024 systems. Possible world semantics is used to interpret our formal languages. Soundness results are obtained for every tableau system and completeness results for a large subclass of these.

Place, publisher, year, edition, pages
Torun: The Nicolaus Copernicus University Press, 2009
Keyword
Counterfactuals, subjunctive conditionals, conditional logic, modal logic, semantic tableau, analytic tableau, Robert Stalnaker, David Lewis, Melvin Fitting, Graham Priest
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
urn:nbn:se:su:diva-31685 (URN)10.12775/LLP.2009.006 (DOI)
Available from: 2009-11-24 Created: 2009-11-24 Last updated: 2015-12-30Bibliographically approved
2. Dyadic Deontic Logic and Semantic Tableaux
Open this publication in new window or tab >>Dyadic Deontic Logic and Semantic Tableaux
2009 (English)In: Logic and Logical Philosophy, ISSN 1425-3305, Vol. 18, no 3-4, 221-252 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to develop a class of semantic tableau systems for some dyadic deontic logics. We will consider 16 different pure dyadic deontic tableau systems and 32 different alethic dyadic deontic tableau systems. Possible world semantics is used to interpret our formal languages. Some relationships between our systems and well known dyadic deontic logics in the literature are pointed out and soundness results are obtained for every tableau system. Completeness results are obtained for all 16 pure dyadic deontic systems and for 16 alethic dyadic deontic systems.

Place, publisher, year, edition, pages
Torun: The Nicolaus Copernicus University Press, 2009
Keyword
dyadic deontic logic, modal logic, semantic tableau, analytic tableau, conditional obligation, commitment, Lennart Åqvist, Melvin Fitting, Graham Priest
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
urn:nbn:se:su:diva-42279 (URN)10.12775%2FLLP.2009.011 (DOI)
Available from: 2010-08-20 Created: 2010-08-20 Last updated: 2015-12-30Bibliographically approved
3. Commitment: some formal interpretations
Open this publication in new window or tab >>Commitment: some formal interpretations
2012 (English)In: Disputatio, ISSN 0873-626X, E-ISSN 2182-2875, Vol. IV, no 33, 445-457 p.Article in journal (Refereed) Published
Abstract [en]

We often use sentences that seem conditional in nature when we reason about normative issues, e.g. ‘If you have promised to do something, you should keep your promise’ and ‘If you have done something bad, you should apologize’. We seem to think that promise-making in some sense commits us to promise-keeping and that acting bad in some sense creates an obligation to apologize. It is, however, not obvious how we should symbolize such sentences in a formal language. The purpose of this essay is to investigate some different possible formalizations of different conditional obligation sentences. I consider seven different interpretations of the concept of commitment or conditional obligation and I say something about the logical properties of these different interpretations.

Keyword
Commitment, conditional obligation, deontic logic, dyadic deontic logic, conditional norms
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
urn:nbn:se:su:diva-80823 (URN)
Available from: 2012-10-15 Created: 2012-09-29 Last updated: 2017-12-07Bibliographically approved
4. Bimodal Logic
Open this publication in new window or tab >>Bimodal Logic
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.

Keyword
Bimodal logic, modal logic, epistemic logic, deontic logic, tense logic
National Category
Philosophy
Research subject
Theoretical Philosophy
Identifiers
urn:nbn:se:su:diva-81229 (URN)10.5840/pjphil20126214 (DOI)
Available from: 2012-10-22 Created: 2012-10-15 Last updated: 2017-12-07Bibliographically approved
5. Temporal alethic–deontic logic and semantic tableaux
Open this publication in new window or tab >>Temporal alethic–deontic logic and semantic tableaux
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.

Keyword
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:nbn:se:su:diva-77037 (URN)10.1016/j.jal.2012.03.002 (DOI)000305772600001 ()
Available from: 2012-05-29 Created: 2012-05-29 Last updated: 2017-12-07Bibliographically approved

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