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See detailA Representation Theorem for Abstract Cumulative Aggregation
Ambrossio, Diego Agustin UL; Parent, Xavier UL; van der Torre, Leon UL

Report (2016)

From any two conditional obligations “X if A” and “Y if B”, cumulative aggregation derives the combined obligation “X ∪ Y if A ∪ (B \ X)”, whereas simple aggregation derives the obligation “X ∪ Y if A ∪ ... [more ▼]

From any two conditional obligations “X if A” and “Y if B”, cumulative aggregation derives the combined obligation “X ∪ Y if A ∪ (B \ X)”, whereas simple aggregation derives the obligation “X ∪ Y if A ∪ B”. We propose FC systems consisting of cumulative aggregation together with factual detachment, and we give a representation result for FC systems, as well as for FA systems consisting of simple aggregation together with factual detachment. We relate FC and FA systems to each other and to input/output logics recently introduced by Parent and van der Torre. [less ▲]

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See detailCumulative Aggregation
Ambrossio, Diego Agustin UL; Parent, Xavier UL; van der Torre, Leon UL

in Deontic Logic and Normative Systems (2016)

From any two conditional obligations “X if A” and “Y if B”, cumulative aggregation derives the combined obligation “X ∪ Y if A ∪ (B\X)”, whereas simple aggregation derives the obligation “X ∪ Y if A ∪ B” ... [more ▼]

From any two conditional obligations “X if A” and “Y if B”, cumulative aggregation derives the combined obligation “X ∪ Y if A ∪ (B\X)”, whereas simple aggregation derives the obligation “X ∪ Y if A ∪ B”. We propose FC systems consisting of cumulative aggregation together with factual detachment, and we give a representation result for FC systems, as well as for FA systems consisting of simple aggregation together with factual detachment. We relate FC and FA systems to each other and to input/output logics recently introduced by Parent and van der Torre. [less ▲]

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See detailCompleteness of Aqvist's systems E and F
Parent, Xavier UL

in Review of Symbolic Logic (2015), 8(1), 164-177

This paper tackles an open problem posed by Åqvist. It is the problem of whether his dyadic deontic systems E and F are complete with respect to their intended Hanssonian preference- based semantics. It ... [more ▼]

This paper tackles an open problem posed by Åqvist. It is the problem of whether his dyadic deontic systems E and F are complete with respect to their intended Hanssonian preference- based semantics. It is known that there are two different ways of interpreting what it means for a world to be best or top-ranked among alternatives. This can be understood as saying that it is optimal among them, or maximal among them. First, it is established that, under either the maximality rule or the optimality rule, E is sound and complete with respect to the class of all preference models, the class of those in which the betterness relation is reflexive, and the class of those in which it is total. Next, an analogous result is shown to hold for F. That is, it is established that, under either rule, F is sound and complete with respect to the class of preference models in which the betterness relation is limited, the class of those in which it is limited and reflexive, and the class of those in which it is limited and total. [less ▲]

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See detailSing and Dance!
van der Torre, Leon UL; Parent, Xavier UL

in Sing and Dance! (2014)

Makinson and van der Torre [13] introduce a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The ... [more ▼]

Makinson and van der Torre [13] introduce a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe[19,20] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Second, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and completeness theorems for the proposed systems with respect to their intended semantics. [less ▲]

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See detailSing and Dance!" - Input/Output Logics without Weakening
Parent, Xavier UL; Torre, Leendert W. N. Van Der

in Deontic Logic and Normative Systems - 12th International Conference DEON 2014, Ghent, Belgium, July 12-15, 2014. Proceedings (2014)

Makinson and van der Torre [14] introduce a number of in- put/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The ... [more ▼]

Makinson and van der Torre [14] introduce a number of in- put/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe [20,21] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Sec- ond, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and complete- ness theorems for the proposed systems with respect to their intended semantics. [less ▲]

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See detailDeontic logic and Normative Systems - DEON2014
Parent, Xavier UL; Mariani, Fabrizio; Grossi, Davide et al

Book published by Springer (2014)

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See detailIntuitionistic basis for IOL
Parent, Xavier UL; van der Torre, Leon UL; Gabbay, Dov M. UL

in Hansson, Sven Ove (Ed.) David Makinson's outsanding contribution to non-classical logic (2014)

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See detailMaximality vs. Optimality in Dyadic Deontic Logic
Parent, Xavier UL

in J. Philosophical Logic (2014), 43(6), 1101--1128

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent- worlds, which underpins such ... [more ▼]

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent- worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief resultofthispaperconcernsA ̊qvist’ssystemFsupplementedwiththeprinciple(CM)of cautious monotony. It is established that, under the maximality rule, F+(CM) is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth (for maximality). From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F+(CM) is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth (for optimality). Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity. [less ▲]

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See detailInput/output logic
Parent, Xavier UL; van der Torre, Leon UL

in van der Torre, Leon; Gabbay, Dov M.; Horty, Jeff (Eds.) et al Handbook of Deontic Logic (2013)

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See detailHandbook of Deontic logic and Normative Systems
Gabbay, Dov; Horty, Jeff; Parent, Xavier UL et al

Book published by College Publication (2013)

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See detailNormative Reasoning and Consequence
Broersen, Jan; Cranefield, Stephen; Elrakaiby, Yehia UL et al

in Normative Multi-Agent Systems (2013)

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See detailContrary-To-Duties in Games
Turrini, Paolo UL; Parent, Xavier UL; van der Torre, Leon UL et al

in Logic Programs, Norms and Action: Essays in Honor of Marek J. Sergot on the Occasion of His 60th Birthday (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) (2012)

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See detailWhy Be Afraid of Identity?
Parent, Xavier UL

in Logic Programs, Norms and Action (2012)

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See detailTwo dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones-Pörn deontic logic system]
Boer, Mathijs De; Gabbay, Dov M. UL; Parent, Xavier UL et al

in Synthese (2012), 187(2), 623--660

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See detailMoral particularism in the light of deontic logic
Parent, Xavier UL

in Artificial Intelligence & Law (2011), 19(2-3), 75-98

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See detailMoral Particularism and Deontic Logic
Parent, Xavier UL

in Sartor, Giovanni; Governatori, Guido (Eds.) Proceedings of the International Conference on Deontic Logic in Computer Science (2010)

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See detailInput/output logics
Parent, Xavier UL; van der Torre, Leon UL

in Abstract book of 9th De Morgan Workshop on Deontic Logic (2009)

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Exa mples ... [more ▼]

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Exa mples arise in contexts of conditional obligations, goals, ideals, preferences , actions, and beliefs. Our purpose is to develop a theory of such input/output operations . Four are singled out: simple- minded, basic (making intelligent use of disjunctiv e inputs), simple-minded reusable (in which outputs may be recycled as inputs), and b asic reusable. They are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels [less ▲]

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See detailA complete axiom set for Hansson's deontic logic DSDL2
Parent, Xavier UL

in Logic Journal of the IGPL (2009)

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