@incollection {2020, title = {Adaptive Deontic Logics}, booktitle = {Handbook of Deontic Logic and Normative Systems}, volume = {2}, year = {In Press}, publisher = {College Publications}, edition = {1}, author = {Van De Putte, Frederik and Beirlaen, Mathieu and Meheus, Joke} } @article {JMFC:iadl, title = {Non-Adjunctive Deontic Logics That Validate Aggregation as Much as Possible}, journal = {Journal of Applied Logic}, year = {In Press}, author = {Meheus, Joke and Beirlaen, Mathieu and Van De Putte, Frederik and Stra{\ss}er, Christian} } @article {2068, title = {Adaptive Deontic Logics: A Survey}, journal = {IfCoLog Journal of Logics and their Applications}, volume = {6}, number = {3}, year = {2019}, pages = {523-608}, chapter = {523}, url = {http://www.collegepublications.co.uk/downloads/ifcolog00032.pdf}, author = {Van De Putte, Frederik and Beirlaen, Mathieu and Meheus, Joke} } @article {strasser2014dynamic, title = {Adaptive Logic Characterizations of Input/output Logic}, journal = {Studia Logica}, volume = {104}, year = {2016}, pages = {869-916}, chapter = {869}, abstract = {

We translate the unconstrained and constrained input/output-logics from [17, 18] to reflexive modal logics, using adaptive logics for the constrained case. The resulting reformulation has various advantages. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our modal framework gives naturally rise to useful variants. Finally, the modal logics display a gain in expressive power over their original counterparts in the input/output framework.

}, author = {Stra{\ss}er, Christian and Beirlaen, Mathieu and Van De Putte, Frederik} } @article {MCJ:iadlnc, title = {An Inconsistency-Adaptive Deontic Logic for Normative Conflicts}, journal = {Journal of Philosophical Logic}, volume = {42}, number = {2}, year = {2013}, pages = {285{\textendash}315}, abstract = {

We present the inconsistency-adaptive deontic logic \sys{DP}$^r$, a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts. On the other hand, \sys{DP}$^r$ still verifies all intuitively reliable inferences valid in Standard Deontic Logic (\sys{SDL}). \sys{DP}$^r$ interprets a given premise set ‘as normally as possible’ with respect to \sys{SDL}. Whereas some \sys{SDL}-rules are verified unconditionally by \sys{DP}$^r$, others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of \sys{DP}$^r$

}, doi = {http://dx.doi.org/10.1007/s10992-011-9221-3}, author = {Beirlaen, Mathieu and Stra{\ss}er, Christian and Meheus, Joke} } @article {beirlaen2013non, title = {Non-monotonic reasoning with normative conflicts in multi-agent deontic logic}, journal = {Journal of Logic and Computation}, volume = {24}, number = {6}, year = {2013}, pages = {1179{\textendash}1207}, abstract = {

We present two multi-agent deontic logics that consistently accommodate various types of normative conflicts. Its language features modal operators for obligation and permission, and for the realization of individual and collective actions. The logic is non-classical since it makes use of a paraconsistent and paracomplete negation connective. Moreover, it is non-monotonic due to its definition within the adaptive logics framework for defeasible reasoning. The logic is equipped with a defeasible proof theory and semantics.

}, doi = {10.1093/logcom/exs059}, author = {Beirlaen, Mathieu and Stra{\ss}er, Christian} } @article {3152453, title = {Two adaptive logics of norm-propositions}, journal = {JOURNAL OF APPLIED LOGIC}, volume = {11}, number = {2}, year = {2013}, pages = {147{\textendash}168}, abstract = {

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in order to meet (ii). This results in the adaptive logics LNPrLNPr and LNPmLNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPrLNPr and LNPmLNPm are equipped with a preferential semantics and a dynamic proof theory.

}, issn = {1570-8683}, doi = {http://dx.doi.org/10.1016/j.jal.2013.02.001}, author = {Beirlaen, Mathieu and Stra{\ss}er, Christian} } @proceedings {2973606, title = {An {A}ndersonian deontic logic with contextualized sanctions}, journal = {11th International Conference on Deontic Logic in Computer Science, DEON2012}, year = {2012}, pages = {151-169}, publisher = {Springer}, abstract = {

We present a refinement of Anderson{\textquoteright}s reduction of deontic logic to modal logic with only alethic modalities. The refined proposal contextualizes the Andersonian sanction constant s by replacing it with a unary sanction operator S that is dependent on the concrete normative requirement that is violated. A formula S B is then for instance interpreted as ldquo B causes a sanctionrdquo or as ldquo B provides a reason for (the applicability of) a sanctionrdquo. Due to its modified sanction operator, the resulting logic DSL invalidates some instances of the inheritance principle. This gives rise to new interesting features. For instance, DSL consistently allows for the presence of conflicting obligations. Moreover, it provides novel insights in various central {\textquoteleft}paradoxes{\textquoteright} in deontic logic such as the Ross paradox, the paradox of the good Samaritan, and Forrester{\textquoteright}s {\textquoteleft}gentle murderer{\textquoteright} paradox.

}, isbn = {9783642315695}, author = {Stra{\ss}er, Christian and Beirlaen, Mathieu}, editor = {Agotnes, Thomas and Broersen, Jan and Elgesem, Dag} } @article {CJM:demi, title = {Tolerating Deontic Conflicts by Adaptively Restricting Inheritance}, journal = {Logique et Analyse}, volume = {219}, year = {2012}, pages = {477-506}, abstract = {

In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics DPM that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of our normative reasoning by their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts.

}, author = {Stra{\ss}er, Christian and Meheus, Joke and Beirlaen, Mathieu} } @phdthesis {PhD_Mathieu, title = {Tolerating Normative Conflicts in Deontic Logic.}, year = {2012}, month = {September 13}, publisher = {Ghent University}, type = {phd}, author = {Beirlaen, Mathieu} } @incollection {Beirlaen2012a, title = {Towards More Conflict-Tolerant Deontic Logics}, booktitle = {Logic, Philosophy and History of Science in Belgium II}, year = {2012}, pages = {1-8}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e}}, address = {Brussel}, abstract = {

In Ethical Consistency, Bernard Williams vindicated the possibility of moral conflicts; he proposed to consistently allow for the presence of such conflicts within the logic of ought. In determining the nature of moral conflict, Williams stressed its contingency. In this paper, Williams’ characterization of moral conflict is defended. However, Williams’ solution for consistently allowing for such conflicts within the logic of ought is shown to be too crude. Whereas Williams rejects all applications of the agglomeration rule in the logic of ought, it is shown that a more sophisticated approach is needed. An alternative solution is presented in which the application of the agglomeration rule is made conditional upon the principle that" oughtimplies can."

}, author = {Beirlaen, Mathieu}, editor = {Van Kerkhove, Bart and Libert, Thierry and Vanpaemel, Geert and Marage, Pierre} } @article {Beirlaen2012, title = {Understanding Human Agency, by {E}rasmus {M}ayr (review; in Dutch)}, journal = {Tijdschrift voor Filosofie}, volume = {2}, year = {2012}, pages = {383-385}, author = {Beirlaen, Mathieu} } @incollection {3126287, title = {A unifying framework for reasoning about normative conflicts}, booktitle = {The logica yearbook 2011}, year = {2012}, pages = {1{\textendash}14}, publisher = {College Publications}, abstract = {

First, two context-dependent desiderata are presented for devising calculi of deontic logic that can consistently accommodate normative conflicts. Conflict-tolerant deontic logics (CTDLs) can be evaluated by their treatment of the trade-off between these desiderata. Next, it is argued that CTDLs defined within the standard format for adaptive logics are particularly good at overcoming this trade-off.

}, isbn = {9781848900714}, author = {Beirlaen, Mathieu}, editor = {Pelis, Michal and Puncochar, Vit} } @article {Beirlaen2011, title = {Aristotle{\textquoteright}s Modal Proofs, by {A}driane {R}ini (review; in Dutch)}, journal = {Tijdschrift voor Filosofie}, volume = {4}, number = {73}, year = {2011}, pages = {749-751}, author = {Beirlaen, Mathieu} } @article {1970192, title = {Ethical consistency and the logic of ought}, journal = {Theoretical and applied ethics}, volume = {1}, number = {3}, year = {2011}, pages = {45{\textendash}51}, abstract = {

In Ethical Consistency, Bernard Williams vindicated the possibility of moral conflicts; he proposed to consistently allow for the presence of such conflicts within the logic of {\textquoteright}ought{\textquoteright}. In determining the nature of moral conflict, Williams stressed its contingency. In this paper, Williams{\textquoteright} characterization of moral conflict is defended. However, Williams{\textquoteright} solution for consistently allowing for such conflicts within the logic of {\textquoteright}ought{\textquoteright} is shown to be too crude. Whereas Williams rejects all applications of the agglomeration rule in the logic of {\textquoteright}ought{\textquoteright}, it is shown that a more sophisticated approach is needed. An alternative solution is presented in which the application of the agglomeration rule is made conditional upon the principle that {\textacutedbl}ought implies can{\textacutedbl}.

}, issn = {2156-7174}, author = {Beirlaen, Mathieu} } @proceedings {1861627, title = {A paraconsistent multi-agent framework for dealing with normative conflicts}, journal = {12th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA XII)}, year = {2011}, pages = {312-329}, publisher = {Springer}, abstract = {

In a multi-agent deontic setting, normative conflicts can take a variety of different logical forms. In this paper, we present a very general characterization of such conflicts, including both intra- and inter-agent normative conflicts, conflicts between groups of agents, conflicts between obligations and permissions, and conflicts between contradictory norms. In order to account for the consistent possibility of this wide variety of conflict-types, we present a paraconsistent deontic logic, i.e. a logic that invalidates the classical principle of non-contradiction. Next, we strengthen this logic within the adaptive logics framework for defeasible reasoning. The resulting inconsistency-adaptive deontic logic interprets a given set of norms {\textquoteright}as consistently as possible{\textquoteright}.

}, isbn = {9783642223587}, url = {http://dx.doi.org/10.1007/978-3-642-22359-4}, author = {Beirlaen, Mathieu and Stra{\ss}er, Christian}, editor = {Leite, Joao and Torroni, Paolo and Agotnes, Thomas and Boella, Guido and van der Torre, Leon} } @conference {JMF:adera, title = {Avoiding Deontic Explosion by Contextually Restricting Aggregation}, booktitle = {Proceedings of the 10th International Conference on Deontic Logic in Computer Science (DEON 2010)}, year = {2010}, publisher = {Springer}, organization = {Springer}, address = {Dordrecht}, abstract = {

In this paper, we present an adaptive logic for deontic conflicts, called \sys{P2.1}$^r$, that is based on Goble{\textquoteright}s logic \sys{SDL}$a$\sys{P}$e${\textendash}-a bimodal extension of Goble{\textquoteright}s logic \sys{P} that invalidates aggregation for all \emph{prima facie} obligations. The logic \sys{P2.1}$^r$ has several advantages with respect to \sys{SDL}$a$\sys{P}$e$. For consistent sets of obligations it yields the same results as Standard Deontic Logic and for inconsistent sets of obligations, it validates aggregation {\textquoteleft}{\textquoteleft}as much as possible{\textquoteright}{\textquoteright}. It thus leads to a richer consequence set than \sys{SDL}$a$\sys{P}$e$. The logic \sys{P2.1}$^r$ avoids Goble{\textquoteright}s criticisms against other non-adjunctive systems of deontic logic. Moreover, it can handle all the {\textquoteleft}toy examples{\textquoteright} from the literature as well as more complex ones.

}, doi = {http://dx.doi.org/10.1007/978-3-642-14183-6\_12}, author = {Meheus, Joke and Beirlaen, Mathieu and Van De Putte, Frederik}, editor = {Governatori, Guido and Sartor, Giovanni} } @article {1096460, title = {Report LRR10: Logic, reasoning and rationality}, journal = {The Reasoner}, volume = {4}, number = {11}, year = {2010}, pages = {165{\textendash}166}, url = {http://www.kent.ac.uk/secl/philosophy/jw/TheReasoner/vol4/TheReasoner-4(11).pdf}, author = {Beirlaen, Mathieu and Gauderis, Tjerk and Gervais, Raoul and Kosolosky, Laszlo} } @article {strasser2010towards, title = {Towards more conflict-tolerant deontic logics by relaxing the interdefinability between obligations and permissions}, year = {2010}, abstract = {

While conflict-tolerant logics (CTDLs) usually allow for obligation- obligation conflicts, they fall short of tolerating obligation-permission con- flicts (OP-conflicts) of the type OA \&\#8743; P\&\#172; A. Moreover, for the sake of conflict-tolerance these logics usually do not validate the very intuitive principle (D), OA \&\#8835; PA. We demonstrate in this paper that by relaxing the interdefinability between obligations and permission PA =df \&\#172;O\&\#172;A that is characteristic for most deontic logics, the logics get more conflict-tolerant since they allow for OP-conflicts. Moreover, this way they can be equipped with (D) without the need to sacrifice conflict-tolerance. In this paper we offer a generic procedure that transforms a given CTDL into a logic that tolerates OP-conflicts and validates (D).

}, author = {Stra{\ss}er, Christian and Beirlaen, Mathieu} }